The following table 3 gives the classification of each ODE from Maple ODE advisor with a link to each ODE page as well. Clicking on the problem opens a new page that shows the result.
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result |
| ODE 1 |
\(y'(x)=a f(x)\) [_quadrature] Solution method Separable ODE, Dependent variable missing Maple ✓ |
| ODE 2 |
\(y'(x)=y(x)+x+\sin (x)\) [[_linear, `class A`]] Solution method Linear ODE Maple ✓ |
| ODE 3 |
\(y'(x)=x^2+2 y(x)+3 \cosh (x)\) [[_linear, `class A`]] Solution method Linear ODE Maple ✓ |
| ODE 4 |
\(y'(x)=a+b x+c y(x)\) [[_linear, `class A`]] Solution method Linear ODE Maple ✓ |
| ODE 5 |
\(y'(x)=a \cos (b x+c)+k y(x)\) [[_linear, `class A`]] Solution method Linear ODE Maple ✓ |
| ODE 6 |
\(y'(x)=a \sin (b x+c)+k y(x)\) [[_linear, `class A`]] Solution method Linear ODE Maple ✓ |
| ODE 7 |
\(y'(x)=a+b e^{k x}+c y(x)\) [[_linear, `class A`]] Solution method Linear ODE Maple ✓ |
| ODE 8 |
\(y'(x)=x \left (x^2-y(x)\right )\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 9 |
\(y'(x)=x \left (a y(x)+e^{-x^2}\right )\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 10 |
\(y'(x)=x^2 \left (a x^3+b y(x)\right )\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 11 |
\(y'(x)=a x^n y(x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 12 |
\(y'(x)=y(x) \cos (x)+\sin (x) \cos (x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 13 |
\(y'(x)=y(x) \cos (x)+e^{\sin (x)}\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 14 |
\(y'(x)=y(x) \cot (x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 15 |
\(y'(x)=1-y(x) \cot (x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 16 |
\(y'(x)=x \csc (x)-y(x) \cot (x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 17 |
\(y'(x)=y(x) (\cot (x)+2 \csc (2 x))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 18 |
\(y'(x)=\sec (x)-y(x) \cot (x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 19 |
\(y'(x)=y(x) \cot (x)+e^x \sin (x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 20 |
\(y'(x)+2 y(x) \cot (x)+\csc (x)=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 21 |
\(y'(x)=4 x \csc (x) \sec ^2(x)-2 y(x) \cot (2 x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 22 |
\(y'(x)=2 \left (\cos (2 x) \cot ^2(x)-y(x) \csc (2 x)\right )\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 23 |
\(y'(x)=4 x \csc (x) \left (y(x)+\sin ^3(x)\right )\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 24 |
\(y'(x)=4 x \csc (x) \left (y(x)-\tan ^2(x)+1\right )\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 25 |
\(y'(x)=y(x) \sec (x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 26 |
\(y'(x)+\tan (x)=(1-y(x)) \sec (x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 27 |
\(y'(x)=y(x) \tan (x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 28 |
\(y'(x)=y(x) \tan (x)+\cos (x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 29 |
\(y'(x)=\cos (x)-y(x) \tan (x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 30 |
\(y'(x)=\sec (x)-y(x) \tan (x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 31 |
\(y'(x)=y(x) \tan (x)+\sin (2 x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 32 |
\(y'(x)=\sin (2 x)-y(x) \tan (x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 33 |
\(y'(x)=2 y(x) \tan (x)+\sin (x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 34 |
\(y'(x)=2 (y(x) \tan (2 x)+\sec (2 x)+1)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 35 |
\(y'(x)=3 y(x) \tan (x)+\csc (x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 36 |
\(y'(x)=y(x) (a+\sin (\log (x))+\cos (\log (x)))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 37 |
\(y'(x)=6 e^{2 x}-y(x) \tanh (x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 38 |
\(y'(x)=y(x) f'(x)+f(x) f'(x)\) odeadvisor timed out Solution method Linear ODE Maple ✓ |
| ODE 39 |
\(y'(x)=f(x)+g(x) y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 40 |
\(y'(x)=x^2-y(x)^2\) [_Riccati] Solution method Series solution to \(y'(x)=f(x,y(x))\), case \(f(x,y)\) analytic Maple ✓ |
| ODE 41 |
\(f(x)^2+y'(x)=f'(x)+y(x)^2\) odeadvisor timed out Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 42 |
\(y'(x)-x+1=y(x) (y(x)+x)\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 43 |
\(y'(x)=(y(x)+x)^2\) [[_homogeneous, `class C`], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 44 |
\(y'(x)=(x-y(x))^2\) [[_homogeneous, `class C`], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 45 |
\(y'(x)=(x-y(x))^2+3 (y(x)-x+1)\) [[_homogeneous, `class C`], _Riccati] Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\) Maple ✓ |
| ODE 46 |
\(y'(x)=-\left (x^2+1\right ) y(x)+y(x)^2+2 x\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 47 |
\(y'(x)=x \left (x^3+2\right )-\left (2 x^2-y(x)\right ) y(x)\) [[_1st_order, _with_linear_symmetries], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 48 |
\(y'(x)=x \left (2-x^3\right )+\left (2 x^2-y(x)\right ) y(x)+1\) [[_1st_order, _with_linear_symmetries], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 49 |
\(y'(x)=\cos (x)-y(x) (\sin (x)-y(x))\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 50 |
\(y'(x)=y(x) (y(x)+\sin (2 x))+\cos (2 x)\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 51 |
\(y'(x)=x f(x) y(x)+f(x)+y(x)^2\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 52 |
\(y'(x)=(-4 y(x)+x+3)^2\) [[_homogeneous, `class C`], _Riccati] Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\) Maple ✓ |
| ODE 53 |
\(y'(x)=(9 y(x)+4 x+1)^2\) [[_homogeneous, `class C`], _Riccati] Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\) Maple ✓ |
| ODE 54 |
\(y'(x)=3 \left (a+b y(x)^2+b x\right )\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 55 |
\(y'(x)=a+b y(x)^2\) [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 56 |
\(y'(x)=a x+b y(x)^2\) [[_Riccati, _special]] Solution method Riccati ODE, Main form Maple ✓ |
| ODE 57 |
\(y'(x)=a+b x+c y(x)^2\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 58 |
\(y'(x)=a x^{n-1}+b x^{2 n}+c y(x)^2\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 59 |
\(y'(x)=a x^2+b y(x)^2\) [[_Riccati, _special]] Solution method Riccati ODE, Main form Maple ✓ |
| ODE 60 |
\(y'(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2\) [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 61 |
\(y'(x)=a y(x)+b y(x)^2+f(x)\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✗ |
| ODE 62 |
\(y'(x)=a (x-y(x)) y(x)+1\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 63 |
\(y'(x)=a y(x)^2+f(x)+g(x) y(x)\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✗ |
| ODE 64 |
\(y'(x)=x y(x) (y(x)+3)\) [_separable] Solution method The Bernoulli ODE Maple ✓ |
| ODE 65 |
\(y'(x)=-x^3+\left (2 x^2+1\right ) y(x)-x y(x)^2-x+1\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 66 |
\(y'(x)=x \left (x^2 y(x)-y(x)^2+2\right )\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 67 |
\(y'(x)=-\left ((1-x) y(x)^2\right )+(1-2 x) y(x)+x\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 68 |
\(y'(x)=a x y(x)^2\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 69 |
\(y'(x)=x^n \left (a+b y(x)^2\right )\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 70 |
\(y'(x)=a x^m+b x^n y(x)^2\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 71 |
\(y'(x)=y(x) (a+b y(x) \cos (k x))\) [_Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 72 |
\(y'(x)=\sin (x) \left (2 \sec ^2(x)-y(x)\right )\) [_linear] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 73 |
\(y'(x)+4 \csc (x)=y(x)^2 \sin (x)+y(x) (3-\cot (x))\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 74 |
\(y'(x)=y(x) \sec (x)+(\sin (x)-1)^2\) [_linear] Solution method The Bernoulli ODE Maple ✓ |
| ODE 75 |
\(y'(x)+\left (1-y(x)^2\right ) \tan (x)=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 76 |
\(y'(x)=f(x)+g(x) y(x)+h(x) y(x)^2\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✗ |
| ODE 77 |
\(y'(x)=f(x) \left (a+b y(x)+c y(x)^2\right )\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 78 |
\(y(x)^2 (a x+y(x))+y'(x)\) [_Abel] Solution method Abel ODE, First kind Maple ✓ |
| ODE 79 |
\(y'(x)=y(x)^2 \left (a e^x+y(x)\right )\) [_Abel] Solution method Abel ODE, First kind Maple ✓ |
| ODE 80 |
\(3 a (y(x)+2 x) y(x)^2+y'(x)=0\) [_Abel] Solution method Abel ODE, First kind Maple ✓ |
| ODE 81 |
\(y'(x)=y(x) \left (a+b y(x)^2\right )\) [_quadrature] Solution method The Bernoulli ODE Maple ✓ |
| ODE 82 |
\(y'(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2+\text {a3} y(x)^3\) [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 83 |
\(y'(x)=x y(x)^3\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 84 |
\(y'(x)+y(x) \left (1-x y(x)^2\right )=0\) [_Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 85 |
\(y'(x)=y(x)^2 (a+b x y(x))\) [[_homogeneous, `class G`], _Abel] Solution method Abel ODE, First kind Maple ✓ |
| ODE 86 |
\(y(x)^3 \left (a+4 b^2 x+3 b x^2\right )+y'(x)+3 x y(x)^2=0\) [_Abel] Solution method Abel ODE, First kind Maple ✓ |
| ODE 87 |
\(y'(x)=y(x)^2 \left (x^3 y(x)+1\right )\) [_Abel] Solution method Abel ODE, First kind Maple ✗ |
| ODE 88 |
\(2 x y(x) \left (a x y(x)^2+1\right )+y'(x)=0\) [_Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 89 |
\(y'(x)=y(x)^2-a x \left (1-x^{n-1}\right ) y(x)^3\) [_Abel] Solution method Abel ODE, First kind Maple ✗ |
| ODE 90 |
\(y'(x)=a y(x)^2+x y(x)^3 \left (b+c x^{n-1}\right )\) [_Abel] Solution method Abel ODE, First kind Maple ✗ |
| ODE 91 |
\(y'(x)+y(x) \left (y(x)^2 \sec (x)+\tan (x)\right )=0\) [_Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 92 |
\(y'(x)+y(x)^3 \tan (x) \sec (x)=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 93 |
\(y'(x)=\text {f0}(x)+\text {f1}(x) y(x)+\text {f2}(x) y(x)^2+\text {f3}(x) y(x)^3\) [_Abel] Solution method Abel ODE, First kind Maple ✗ |
| ODE 94 |
\(y'(x)=y(x) \left (y(x)^3 \sec (x)+\tan (x)\right )\) [_Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 95 |
\(y'(x)=a x^{\frac {n}{1-n}}+b y(x)^n\) [[_homogeneous, `class G`], _Chini] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 96 |
\(y'(x)=f(x) y(x)+g(x) y(x)^k\) [_Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 97 |
\(y'(x)=f(x)+g(x) y(x)+h(x) y(x)^n\) [_Chini] Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 98 |
\(y'(x)=f(x) y(x)^m+g(x) y(x)^n\) [NONE] Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 99 |
\(y'(x)=\sqrt {| y(x)| }\) [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 100 |
\(y'(x)=a+\sqrt {\text {A0}+\text {B0} y(x)}+b y(x)\) [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 101 |
\(y'(x)=a x+b \sqrt {y(x)}\) [[_homogeneous, `class G`], _Chini] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 102 |
\(x^3+y'(x)=x \sqrt {x^4+4 y(x)}\) [[_1st_order, _with_linear_symmetries]] Solution method Homogeneous equation, isobaric equation Maple ✓ |
| ODE 103 |
\(y'(x)+2 \left (1-x \sqrt {y(x)}\right ) y(x)=0\) [_Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 104 |
\(y'(x)=\sqrt {a+b y(x)^2}\) [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 105 |
\(y'(x)=y(x) \sqrt {a+b y(x)}\) [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 106 |
\(g(x) (f(x)-y(x)) \sqrt {(y(x)-a) (y(x)-b)}+y'(x)=0\) [`y=_G(x,y')`] Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 107 |
\(y'(x)=\sqrt {X Y}\) [_quadrature] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 108 |
\(y'(x)=\text {R1}\left (x,\sqrt {X}\right ) \text {R2}\left (y(x),\sqrt {Y}\right )\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 109 |
\(y'(x)=\cos ^2(x) \cos (y(x))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 110 |
\(y'(x)=\sec ^2(x) \text {Cosy}(y(x)) \cot (y(x))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 111 |
\(y'(x)=a+b \cos (A x+B y(x))\) [[_homogeneous, `class C`], _dAlembert] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 112 |
\(y'(x)=-\left (1-f'(x)\right ) \cos (y(x))+f'(x)-f(x) \sin (y(x))+1\) odeadvisor timed out Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 113 |
\(g(x) \sin (a y(x))+h(x) \cos (a y(x))+f(x)+y'(x)=0\) [`y=_G(x,y')`] Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 114 |
\(y'(x)=a+b \cos (y(x))\) [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 115 |
\(x \left (\sin (2 y(x))-x^2 \cos ^2(y(x))\right )+y'(x)=0\) [`y=_G(x,y')`] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 116 |
\(y'(x)+\tan (x) \sec (x) \cos ^2(y(x))=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 117 |
\(y'(x)=\cot (x) \cot (y(x))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 118 |
\(y'(x)+\cot (x) \cot (y(x))=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 119 |
\(y'(x)=\sin (x) (\csc (y(x))-\cot (y(x)))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 120 |
\(y'(x)=\tan (x) \cot (y(x))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 121 |
\(y'(x)+\tan (x) \cot (y(x))=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 122 |
\(y'(x)+\sin (2 x) \csc (2 y(x))=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 123 |
\(y'(x)=\tan (x) (\tan (y(x))+\sec (x) \sec (y(x)))\) [`y=_G(x,y')`] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 124 |
\(y'(x)=\cos (x) \sec ^2(y(x))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 125 |
\(y'(x)=\sec ^2(x) \sec ^3(y(x))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 126 |
\(y'(x)=a+b \sin (y(x))\) [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 127 |
\(y'(x)=a+b \sin (A x+B y(x))\) [[_homogeneous, `class C`], _dAlembert] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 128 |
\(y'(x)=\tan (y(x)) (\cos (x) \sin (y(x))+1)\) [`y=_G(x,y')`] Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 129 |
\(y'(x)+\csc (2 x) \sin (2 y(x))=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 130 |
\(f(x)+g(x) \tan (y(x))+y'(x)=0\) [`y=_G(x,y')`] Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 131 |
\(y'(x)=\sqrt {a+b \cos (y(x))}\) [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 132 |
\(y'(x)=e^{y(x)}+x\) [[_1st_order, `_with_symmetry_[F(x),G(x)]`]] Solution method Series solution to \(y'(x)=f(x,y(x))\), case \(f(x,y)\) analytic Maple ✓ |
| ODE 133 |
\(y'(x)=e^{y(x)+x}\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 134 |
\(y'(x)=e^x \left (a+b e^{-y(x)}\right )\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 135 |
\(y'(x)+y(x) \log (x) \log (y(x))=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 136 |
\(y'(x)=x^{m-1} y(x)^{1-n} f\left (a x^m+b y(x)^n\right )\) [[_1st_order, `_with_symmetry_[F(x),G(y)]`]] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 137 |
\(y'(x)=a f(y(x))\) [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 138 |
\(y'(x)=f(a+b x+c y(x))\) [[_homogeneous, `class C`], _dAlembert] Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\) Maple ✓ |
| ODE 139 |
\(y'(x)=f(x) g(y(x))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 140 |
\(y'(x)=\text {Csx}(x) y(x) \sec (x)+\sec ^2(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 141 |
\(2 y'(x)+2 \csc ^2(x)=y(x) \csc (x) \sec (x)-y(x)^2 \sec ^2(x)\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 142 |
\(2 y'(x)=2 \sin ^2(y(x)) \tan (y(x))-x \sin (2 y(x))\) [`y=_G(x,y')`] Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 143 |
\(a x+2 y'(x)=\sqrt {a^2 x^2-4 b x^2-4 c y(x)}\) [[_homogeneous, `class G`]] Solution method Homogeneous equation, isobaric equation Maple ✓ |
| ODE 144 |
\(3 y'(x)=\sqrt {x^2-3 y(x)}+x\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 145 |
\(x y'(x)=\sqrt {a^2-x^2}\) [_quadrature] Solution method Separable ODE, Dependent variable missing Maple ✓ |
| ODE 146 |
\(x y'(x)+y(x)+x=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 147 |
\(x^2+x y'(x)-y(x)=0\) [_linear] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 148 |
\(x y'(x)=x^3-y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 149 |
\(x y'(x)=x^3+y(x)+1\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 150 |
\(x y'(x)=x^m+y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 151 |
\(x y'(x)=x \sin (x)-y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 152 |
\(x y'(x)=x^2 \sin (x)+y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 153 |
\(x y'(x)=x^n \log (x)-y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 154 |
\(x y'(x)=\sin (x)-2 y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 155 |
\(x y'(x)=a y(x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 156 |
\(x y'(x)=a y(x)+x+1\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 157 |
\(x y'(x)=a x+b y(x)\) [_linear] Solution method Homogeneous equation Maple ✓ |
| ODE 158 |
\(x y'(x)=a x^2+b y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 159 |
\(x y'(x)=a+b x^n+c y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 160 |
\(x y'(x)+(3-x) y(x)+2=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 161 |
\((a x+2) y(x)+x y'(x)+x=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 162 |
\(y(x) (a+b x)+x y'(x)=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 163 |
\(x y'(x)=x^3+\left (1-2 x^2\right ) y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 164 |
\(x y'(x)=a x-\left (1-b x^2\right ) y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 165 |
\(\left (2-a x^2\right ) y(x)+x y'(x)+x=0\) [_linear] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 166 |
\(x^2+x y'(x)+y(x)^2=0\) [_rational, _Riccati] Solution method Riccati ODE, Special cases Maple ✓ |
| ODE 167 |
\(x y'(x)=x^2+y(x) (y(x)+1)\) [[_homogeneous, `class D`], _rational, _Riccati] Solution method Riccati ODE, Special cases Maple ✓ |
| ODE 168 |
\(x y'(x)+y(x)^2-y(x)=x^{2/3}\) [_rational, _Riccati] Solution method Riccati ODE, Special cases Maple ✓ |
| ODE 169 |
\(x y'(x)=a+b y(x)^2\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 170 |
\(x y'(x)=a x^2+b y(x)^2+y(x)\) [[_homogeneous, `class D`], _rational, _Riccati] Solution method Riccati ODE, Special cases Maple ✓ |
| ODE 171 |
\(x y'(x)=a x^{2 n}+y(x) (b y(x)+n)\) [_rational, _Riccati] Solution method Riccati ODE, Special cases Maple ✓ |
| ODE 172 |
\(x y'(x)=a x^n+b y(x)+c y(x)^2\) [_rational, _Riccati] Solution method Riccati ODE, Special cases Maple ✓ |
| ODE 173 |
\(x y'(x)=a x^n+b y(x)+c y(x)^2+k\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 174 |
\(a+x y'(x)+x y(x)^2=0\) [_rational, [_Riccati, _special]] Solution method Riccati ODE, Main form Maple ✓ |
| ODE 175 |
\(x y'(x)+y(x) (1-x y(x))=0\) [[_homogeneous, `class G`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 176 |
\(x y'(x)=y(x) (1-x y(x))\) [[_homogeneous, `class D`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 177 |
\(x y'(x)=y(x) (x y(x)+1)\) [[_homogeneous, `class D`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 178 |
\(x y'(x)=a x^3 y(x) (1-x y(x))\) [_Bernoulli] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 179 |
\(x y'(x)=x^3+\left (2 x^2+1\right ) y(x)+x y(x)^2\) [[_homogeneous, `class D`], _rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 180 |
\(x y'(x)=y(x) (2 x y(x)+1)\) [[_homogeneous, `class D`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 181 |
\(y(x) (a x y(x)+2)+b x+x y'(x)=0\) [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 182 |
\(\text {a0}+\text {a1} x+y(x) (\text {a2}+\text {a3} x y(x))+x y'(x)=0\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 183 |
\(a x^2 y(x)^2+x y'(x)+2 y(x)=b\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 184 |
\(\frac {1}{2} (n-m) y(x)+x^m+x^n y(x)^2+x y'(x)=0\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 185 |
\(y(x) \left (a+b x^n y(x)\right )+x y'(x)=0\) [[_homogeneous, `class G`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 186 |
\(x y'(x)=a x^m-b y(x)-c x^n y(x)^2\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 187 |
\(x y'(x)=a x^n (x-y(x))^2-y(x)+2 x\) [[_1st_order, _with_linear_symmetries], _rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 188 |
\(y(x) (1-a y(x) \log (x))+x y'(x)=0\) [_Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 189 |
\(x y'(x)=f(x) \left (x^2-y(x)^2\right )+y(x)\) [[_homogeneous, `class D`], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 190 |
\(x y'(x)=y(x) \left (y(x)^2+1\right )\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 191 |
\(x y'(x)+y(x) \left (1-x y(x)^2\right )=0\) [[_homogeneous, `class G`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 192 |
\(x y'(x)+y(x)=a \left (x^2+1\right ) y(x)^3\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 193 |
\(x y'(x)=a y(x)+b \left (x^2+1\right ) y(x)^3\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 194 |
\(x y'(x)+2 y(x)=a x^{2 k} y(x)^k\) [[_homogeneous, `class G`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 195 |
\(x y'(x)=4 \left (y(x)-\sqrt {y(x)}\right )\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 196 |
\(x y'(x)+2 y(x)=\sqrt {y(x)^2+1}\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 197 |
\(x y'(x)=\sqrt {x^2+y(x)^2}+y(x)\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 198 |
\(x y'(x)=\sqrt {x^2-y(x)^2}+y(x)\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 199 |
\(x y'(x)=x \sqrt {x^2+y(x)^2}+y(x)\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Homogeneous equation, \(xy'(x)=x f(x) g(u)+y(x)\) Maple ✓ |
| ODE 200 |
\(x y'(x)=y(x)-x (x-y(x)) \sqrt {x^2+y(x)^2}\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Homogeneous equation, \(xy'(x)=x f(x) g(u)+y(x)\) Maple ✓ |
| ODE 201 |
\(x y'(x)=a \sqrt {b^2 x^2+y(x)^2}+y(x)\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 202 |
\(\cos (y(x)) \left (\sin (y(x))-3 x^2 \cos (y(x))\right )+x y'(x)=0\) [`y=_G(x,y')`] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 203 |
\(x y'(x)-y(x)+x \cos \left (\frac {y(x)}{x}\right )+x=0\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 204 |
\(x y'(x)=y(x)-x \cos ^2\left (\frac {y(x)}{x}\right )\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 205 |
\(x y'(x)=\left (1-2 x^2\right ) \cot ^2(y(x))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 206 |
\(x y'(x)=y(x)-\cot ^2(y(x))\) [_separable] Solution method Homogeneous equation Maple ✓ |
| ODE 207 |
\(x y'(x)+y(x)+2 x \sec (x y(x))=0\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 208 |
\(x y'(x)-y(x)+x \sec \left (\frac {y(x)}{x}\right )=0\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 209 |
\(x y'(x)=y(x)+x \sec ^2\left (\frac {y(x)}{x}\right )\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 210 |
\(x y'(x)=\sin (x-y(x))\) [`y=_G(x,y')`] Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 211 |
\(x y'(x)=y(x)+x \sin \left (\frac {y(x)}{x}\right )\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 212 |
\(x y'(x)+\tan (y(x))=0\) [_separable] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 213 |
\(x y'(x)+\tan (y(x)+x)+x=0\) [[_1st_order, _with_linear_symmetries]] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 214 |
\(x y'(x)=y(x)-x \tan \left (\frac {y(x)}{x}\right )\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 215 |
\(x y'(x)=\left (y(x)^2+1\right ) \left (x^2+\tan ^{-1}(y(x))\right )\) [`y=_G(x,y')`] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 216 |
\(x y'(x)=x e^{\frac {y(x)}{x}}+y(x)\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 217 |
\(x y'(x)=x e^{\frac {y(x)}{x}}+y(x)+x\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 218 |
\(x y'(x)=y(x) \log (y(x))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 219 |
\(x y'(x)=y(x) (-\log (y(x))+\log (x)+1)\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 220 |
\(x y'(x)+y(x) (-\log (y(x))-\log (x)+1)=0\) [[_homogeneous, `class G`]] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 221 |
\(x y'(x)=y(x)-2 x \tanh \left (\frac {y(x)}{x}\right )\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 222 |
\(n y(x)+x y'(x)=f(x) g\left (x^n y(x)\right )\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 223 |
\(x y'(x)=y(x) f\left (x^m y(x)^n\right )\) [[_homogeneous, `class G`]] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 224 |
\((x+1) y'(x)=(3 x+4) x^3+y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 225 |
\((x+1) y'(x)=2 y(x)+(x+1)^4\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 226 |
\((x+1) y'(x)=n y(x)+e^x (x+1)^{n+1}\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 227 |
\((x+1) y'(x)=a y(x)+b x y(x)^2\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 228 |
\((x+1) y'(x)+(x+1)^4 y(x)^3+y(x)=0\) [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 229 |
\((x+1) y'(x)=y(x) \left (1-x y(x)^3\right )\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 230 |
\((x+1) y'(x)=(x+1) \sqrt {y(x)+1}+y(x)+1\) [[_1st_order, _with_linear_symmetries]] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 231 |
\((a+x) y'(x)=b x\) [_quadrature] Solution method Separable ODE, Dependent variable missing Maple ✓ |
| ODE 232 |
\((a+x) y'(x)=b x+y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 233 |
\((a+x) y'(x)+b x^2+y(x)=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 234 |
\((a+x) y'(x)=2 (a+x)^5+3 y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 235 |
\((a+x) y'(x)=b+c y(x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 236 |
\((a+x) y'(x)=b x+c y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 237 |
\((a+x) y'(x)=y(x) (1-a y(x))\) [_separable] Solution method The Bernoulli ODE Maple ✓ |
| ODE 238 |
\((a-x) y'(x)=y(x)^3 (b+c x)+y(x)\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 239 |
\(2 x y'(x)=2 x^3-y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 240 |
\(2 x y'(x)+1=y(x)^2+4 i x y(x)\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 241 |
\(2 x y'(x)=y(x) \left (y(x)^2+1\right )\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 242 |
\(2 x y'(x)+y(x) \left (y(x)^2+1\right )=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 243 |
\(2 x y'(x)=y(x) \left (-6 y(x)^2+x+1\right )\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 244 |
\(\sqrt {a^2-4 b-4 c y(x)}+a+2 x y'(x)+4 y(x)=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 245 |
\((1-2 x) y'(x)=2 (-3 y(x)+16 x+8)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 246 |
\((2 x+1) y'(x)=4 e^{-y(x)}-2\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 247 |
\(2 (1-x) y'(x)=y(x)+4 \sqrt {1-x} x\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 248 |
\(2 (x+1) y'(x)+(x+1)^4 y(x)^3+2 y(x)=0\) [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 249 |
\(3 x y'(x)=3 x^{2/3}+(1-3 y(x)) y(x)\) [_rational, _Riccati] Solution method Riccati ODE, Special cases Maple ✓ |
| ODE 250 |
\(3 x y'(x)=y(x) \left (x y(x)^3+2\right )\) [[_homogeneous, `class G`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 251 |
\(3 x y'(x)=y(x) \left (3 x y(x)^3 \log (x)+1\right )\) [_Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 252 |
\(x^2 y'(x)=a-y(x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 253 |
\(x^2 y'(x)=a+b x+c x^2+x y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 254 |
\(x^2 y'(x)=a+b x+c x^2-x y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 255 |
\(x^2 y'(x)+(1-2 x) y(x)=x^2\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 256 |
\(x^2 y'(x)=a+b x y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 257 |
\(x^2 y'(x)=y(x) (a+b x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 258 |
\(x^2 y'(x)+(x+2) x y(x)=\left (1-e^{-2 x}\right ) x-2\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 259 |
\(x^2 y'(x)+2 (1-x) x y(x)=e^x \left (2 e^x-1\right )\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 260 |
\(x^2 y'(x)+x^2+x y(x)+y(x)^2=0\) [[_homogeneous, `class A`], _rational, _Riccati] Solution method Homogeneous equation Maple ✓ |
| ODE 261 |
\(x^2 y'(x)=(-y(x)+2 x+1)^2\) [[_homogeneous, `class C`], _rational, _Riccati] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 262 |
\(x^2 y'(x)=a+b y(x)^2\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 263 |
\(x^2 y'(x)=y(x) (a y(x)+x)\) [[_homogeneous, `class A`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 264 |
\(x^2 y'(x)=y(x) (a x+b y(x))\) [[_homogeneous, `class A`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 265 |
\(a x^2+b x y(x)+c y(x)^2+x^2 y'(x)=0\) [[_homogeneous, `class A`], _rational, _Riccati] Solution method Homogeneous equation Maple ✓ |
| ODE 266 |
\(x^2 y'(x)=a+b x^n+x^2 y(x)^2\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 267 |
\(x^2 y'(x)+x y(x) (x y(x)+4)+2=0\) [[_homogeneous, `class G`], _rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 268 |
\(a x (1-x y(x))+x^2 y'(x)+x^2 \left (-y(x)^2\right )+2=0\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 269 |
\(x^2 y'(x)=a+b x^2 y(x)^2\) [[_homogeneous, `class G`], _rational, [_Riccati, _special]] Solution method Riccati ODE, Main form Maple ✓ |
| ODE 270 |
\(x^2 y'(x)=a+b x^n+c x^2 y(x)^2\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 271 |
\(x^2 y'(x)=a+b x y(x)+c x^2 y(x)^2\) [[_homogeneous, `class G`], _rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 272 |
\(x^2 y'(x)=a+b x y(x)+c x^4 y(x)^2\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 273 |
\(x^2 y'(x)+y(x) \left (x^2+y(x)^2-x\right )=0\) [[_homogeneous, `class D`], _rational, _Bernoulli] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 274 |
\(x^2 y'(x)=2 y(x) \left (x-y(x)^2\right )\) [[_homogeneous, `class G`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 275 |
\(x^2 y'(x)=a x^2 y(x)^2-a y(x)^3\) [_rational, _Abel] Solution method Abel ODE, Second kind Maple ✓ |
| ODE 276 |
\(a y(x)^2+b x^2 y(x)^3+x^2 y'(x)=0\) [_rational, _Abel] Solution method Abel ODE, Second kind Maple ✓ |
| ODE 277 |
\(x^2 y'(x)=y(x) \left (a x+b y(x)^3\right )\) [[_homogeneous, `class G`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 278 |
\(x^2 y'(x)+x y(x)+\sqrt {y(x)}=0\) [[_homogeneous, `class G`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 279 |
\(x^2 y'(x)=3 x \tan (y(x))+\sec (y(x))\) [`y=_G(x,y')`] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 280 |
\(\left (1-x^2\right ) y'(x)=-x^2+y(x)+1\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 281 |
\(\left (1-x^2\right ) y'(x)+1=x y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 282 |
\(\left (1-x^2\right ) y'(x)=5-x y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 283 |
\(a+\left (x^2+1\right ) y'(x)+x y(x)=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 284 |
\(a+\left (x^2+1\right ) y'(x)-x y(x)=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 285 |
\(a+\left (1-x^2\right ) y'(x)-x y(x)=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 286 |
\(\left (1-x^2\right ) y'(x)+x y(x)-x=0\) [_separable] Solution method Linear ODE Maple ✓ |
| ODE 287 |
\(\left (1-x^2\right ) y'(x)-x^2+x y(x)=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 288 |
\(\left (1-x^2\right ) y'(x)+x^2+x y(x)=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 289 |
\(\left (x^2+1\right ) y'(x)=x \left (x^2+1\right )-x y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 290 |
\(\left (x^2+1\right ) y'(x)=x \left (3 x^2-y(x)\right )\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 291 |
\(\left (1-x^2\right ) y'(x)+2 x y(x)=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 292 |
\(\left (x^2+1\right ) y'(x)=2 x (x-y(x))\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 293 |
\(\left (x^2+1\right ) y'(x)=2 x \left (x^2+1\right )^2+2 x y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 294 |
\(\left (1-x^2\right ) y'(x)+\cos (x)=2 x y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 295 |
\(\left (x^2+1\right ) y'(x)=\tan (x)-2 x y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 296 |
\(\left (1-x^2\right ) y'(x)=a+4 x y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 297 |
\(\left (x^2+1\right ) y'(x)=y(x) (a+2 b x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 298 |
\(\left (x^2+1\right ) y'(x)=y(x)^2+1\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 299 |
\(\left (1-x^2\right ) y'(x)=1-y(x)^2\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 300 |
\(\left (1-x^2\right ) y'(x)=1-(2 x-y(x)) y(x)\) [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 301 |
\(\left (1-x^2\right ) y'(x)=n \left (y(x)^2-2 x y(x)+1\right )\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 302 |
\(\left (x^2+1\right ) y'(x)+x (1-y(x)) y(x)=0\) [_separable] Solution method The Bernoulli ODE Maple ✓ |
| ODE 303 |
\(\left (1-x^2\right ) y'(x)=x y(x) (a y(x)+1)\) [_separable] Solution method The Bernoulli ODE Maple ✓ |
| ODE 304 |
\(\left (x^2+1\right ) y'(x)=y(x)^2-2 x \left (y(x)^2+1\right ) y(x)+1\) [_rational, _Abel] Solution method Abel ODE, Second kind Maple ✓ |
| ODE 305 |
\(\left (x^2+1\right ) y'(x)+x \sin (y(x)) \cos (y(x))=x \left (x^2+1\right ) \cos ^2(y(x))\) [`y=_G(x,y')`] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 306 |
\(\left (x^2+1\right ) y'(x)=x^2-y(x) \cot ^{-1}(x)+1\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 307 |
\(\left (4-x^2\right ) y'(x)+4 y(x)=(x+2) y(x)^2\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 308 |
\(\left (a^2+x^2\right ) y'(x)=b+x y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 309 |
\(\left (a^2+x^2\right ) y'(x)=\left (\sqrt {a^2+x^2}+x\right ) (b+y(x))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 310 |
\(\left (a^2+x^2\right ) y'(x)+(x-y(x)) y(x)=0\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 311 |
\(\left (a^2+x^2\right ) y'(x)=a^2-2 y(x)^2+3 x y(x)\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 312 |
\(\left (a^2+x^2\right ) y'(x)+b x y(x)^2+x y(x)=0\) [_separable] Solution method The Bernoulli ODE Maple ✓ |
| ODE 313 |
\((1-x) x y'(x)=a+(x+1) y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 314 |
\((1-x) x y'(x)=2 (x y(x)+1)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 315 |
\((1-x) x y'(x)=2 (x y(x)-1)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 316 |
\(x (x+1) y'(x)=(1-2 x) y(x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 317 |
\((1-x) x y'(x)+(2 x+1) y(x)=a\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 318 |
\((1-x) x y'(x)=a+2 (2-x) y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 319 |
\((1-x) x y'(x)-3 x y(x)+y(x)+2=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 320 |
\(x (x+1) y'(x)=\left (x^2+x-1\right ) y(x)+(x+1) \left (x^2-1\right )\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 321 |
\(x^2+(x-3) (x-2) y'(x)+3 x y(x)-8 y(x)=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 322 |
\(x (a+x) y'(x)=y(x) (b+c y(x))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 323 |
\((a+x)^2 y'(x)=2 (a+x) (b+y(x))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 324 |
\(k (-a+y(x)+x)^2+(x-a)^2 y'(x)+y(x)^2=0\) [[_homogeneous, `class C`], _rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 325 |
\((x-a) (x-b) y'(x)+k y(x)=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 326 |
\((x-a) (x-b) y'(x)=y(x) (-a-b+2 x)+(x-a) (x-b)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 327 |
\((x-a) (x-b) y'(x)=c y(x)^2\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 328 |
\(k (y(x)-a) (y(x)-b)+(x-a) (x-b) y'(x)=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 329 |
\(k (-a+y(x)+x) (-b+y(x)+x)+(x-a) (x-b) y'(x)+y(x)^2=0\) [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 330 |
\(2 x^2 y'(x)=y(x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 331 |
\(2 x^2 y'(x)+2 x^2 y(x) \cot (x)+x \cot (x)-1=0\) [_linear] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 332 |
\(2 x^2 y'(x)+x^2 \left (-y(x)^2\right )+2 x y(x)+1=0\) [[_homogeneous, `class G`], _rational, _Riccati] Solution method Homogeneous equation, isobaric equation Maple ✓ |
| ODE 333 |
\(2 x^2 y'(x)=\left (x^2-y(x)^2\right ) (1-x \cot (x))+2 x y(x)\) [[_homogeneous, `class D`], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 334 |
\(2 \left (1-x^2\right ) y'(x)=\sqrt {1-x^2}+(x+1) y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 335 |
\((1-2 x) x y'(x)+(1-4 x) y(x)+1=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 336 |
\((1-2 x) x y'(x)=y(x)^2-(4 x+1) y(x)+4 x\) [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 337 |
\(2 (1-x) x y'(x)+(1-2 x) y(x)+x=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 338 |
\(2 (1-x) x y'(x)+(1-x) y(x)^2+x=0\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 339 |
\(2 \left (x^2+x+1\right ) y'(x)=8 x^2-(2 x+1) y(x)+1\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 340 |
\(4 \left (x^2+1\right ) y'(x)-x^2-4 x y(x)=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 341 |
\(a x^2 y'(x)=a x y(x)+b^2 y(x)^2+x^2\) [[_homogeneous, `class A`], _rational, _Riccati] Solution method Homogeneous equation Maple ✓ |
| ODE 342 |
\(\left (a+b x^2\right ) y'(x)=A+B y(x)^2\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 343 |
\(\left (a+b x^2\right ) y'(x)=c x y(x) \log (y(x))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 344 |
\(x (a x+1) y'(x)+a-y(x)=0\) [_separable] Solution method Linear ODE Maple ✓ |
| ODE 345 |
\((a+b x)^2 y'(x)+y(x)^3 (a+b x)+c y(x)^2=0\) [_rational, _Abel] Solution method Abel ODE, Second kind Maple ✓ |
| ODE 346 |
\(x^3 y'(x)=a+b x^2 y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 347 |
\(x^3 y'(x)=x^2 y(x)-x^2+3\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 348 |
\(x^3 y'(x)=x^4+y(x)^2\) [[_homogeneous, `class G`], _rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 349 |
\(x^3 y'(x)=y(x) \left (x^2+y(x)\right )\) [[_homogeneous, `class D`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 350 |
\(x^3 y'(x)=x^2 (y(x)-1)+y(x)^2\) [[_homogeneous, `class D`], _rational, _Riccati] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 351 |
\(x^3 y'(x)=(x+1) y(x)^2\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 352 |
\(x^3 y'(x)+x^2 y(x) \left (1-x^2 y(x)\right )+20=0\) [[_homogeneous, `class G`], _rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 353 |
\(x^6 \left (-y(x)^2\right )+x^3 y'(x)+(3-2 x) x^2 y(x)+3=0\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 354 |
\(x^3 y'(x)=y(x) \left (2 x^2+y(x)^2\right )\) [[_homogeneous, `class A`], _rational, _Bernoulli] Solution method Homogeneous equation Maple ✓ |
| ODE 355 |
\(x^3 y'(x)=\cos (y(x)) \left (\cos (y(x))-2 x^2 \sin (y(x))\right )\) [`y=_G(x,y')`] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 356 |
\(x \left (x^2+1\right ) y'(x)=a x^2+y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 357 |
\(x \left (1-x^2\right ) y'(x)=a x^2+y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 358 |
\(x \left (x^2+1\right ) y'(x)=a x^3+y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 359 |
\(x \left (x^2+1\right ) y'(x)=a-x^2 y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 360 |
\(x \left (x^2+1\right ) y'(x)=\left (1-x^2\right ) y(x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 361 |
\(x \left (1-x^2\right ) y'(x)=\left (x^2-x+1\right ) y(x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 362 |
\(x \left (1-x^2\right ) y'(x)=a x^3+\left (1-2 x^2\right ) y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 363 |
\(x \left (1-x^2\right ) y'(x)=\left (1-2 x^2\right ) y(x)+\left (1-x^2\right ) x^3\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 364 |
\(x \left (x^2+1\right ) y'(x)=2 \left (1-2 x^2 y(x)\right )\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 365 |
\(x \left (x^2+1\right ) y'(x)=x-\left (5 x^2+3\right ) y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 366 |
\(\left (1-x^2\right ) x y'(x)+\left (1-x^2\right ) y(x)^2+x^2=0\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 367 |
\((1-x) x^2 y'(x)=(2-x) x y(x)-y(x)^2\) [[_homogeneous, `class D`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 368 |
\(2 x^3 y'(x)=y(x) \left (x^2-y(x)^2\right )\) [[_homogeneous, `class A`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 369 |
\(2 x^3 y'(x)=y(x) \left (a y(x)^2+3 x^2\right )\) [[_homogeneous, `class A`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 370 |
\(6 x^3 y'(x)=4 x^2 y(x)+(1-3 x) y(x)^4\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 371 |
\(x y'(x) \left (a+b x+c x^2\right )-y(x) \left (a+b x+c x^2\right )+x^2=y(x)^2\) [[_homogeneous, `class D`], _rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 372 |
\(x^4 y'(x)=y(x) \left (x^3+y(x)\right )\) [[_homogeneous, `class D`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 373 |
\(a^2+x^4 y'(x)+x^4 y(x)^2=0\) [_rational, [_Riccati, _special]] Solution method Riccati ODE, Main form Maple ✓ |
| ODE 374 |
\(x^4 y'(x)+x^3 y(x)+\csc (x y(x))=0\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 375 |
\(\left (1-x^4\right ) y'(x)=2 x \left (1-y(x)^2\right )\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 376 |
\(x \left (1-x^3\right ) y'(x)=2 x-\left (1-4 x^3\right ) y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 377 |
\(x \left (1-x^3\right ) y'(x)=x^2+y(x) (1-2 x y(x))\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 378 |
\(x^2 \left (1-x^2\right ) y'(x)=y(x) \left (x-3 x^3 y(x)\right )\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 379 |
\(x \left (1-2 x^3\right ) y'(x)=2 \left (1-x^3\right ) y(x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 380 |
\(\left (y'(x)+y(x)^2\right ) \left (a+b x+c x^2\right )^2+A=0\) [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 381 |
\(x^5 y'(x)=1-3 x^4 y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 382 |
\(x \left (1-x^4\right ) y'(x)=\left (1-x^4\right ) y(x)+2 x \left (x^2-y(x)^2\right )\) [[_homogeneous, `class D`], _rational, _Riccati] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 383 |
\(x^7 y'(x)+5 x^3 y(x)^2+2 \left (x^2+1\right ) y(x)^3=0\) [_rational, _Abel] Solution method Abel ODE, First kind Maple ✓ |
| ODE 384 |
\(x^n y'(x)=a+b x^{n-1} y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 385 |
\(x^n y'(x)=x^{2 n-1}-y(x)^2\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 386 |
\(y(x) \left (x^{n-1}+y(x)\right )+x^n y'(x)+x^2=0\) [_Riccati] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 387 |
\((1-n) x^{n-1}+x^{2 n-2}+x^n y'(x)+y(x)^2=0\) [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 388 |
\(x^n y'(x)=a^2 x^{2 n-2}+b^2 y(x)^2\) [[_homogeneous, `class G`], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 389 |
\(x^n y'(x)=x^{n-1} \left (a x^{2 n}-b y(x)^2+n y(x)\right )\) [_rational, _Riccati] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 390 |
\(x^{2 n} y'(x)=-n x^{n-1}+x^n y(x) \left (x^{2 n} y(x)^2-3 x^n y(x)+1\right )+1\) [_Abel] Solution method Abel ODE, First kind Maple ✓ |
| ODE 391 |
\(x^k y'(x)=a x^m+b y(x)^n\) [_Chini] Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 392 |
\(\sqrt {x^2+1} y'(x)=2 x-y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 393 |
\(\sqrt {1-x^2} y'(x)=y(x)^2+1\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 394 |
\(\left (x-\sqrt {x^2+1}\right ) y'(x)=y(x)+\sqrt {y(x)^2+1}\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 395 |
\(\sqrt {a^2+x^2} y'(x)+y(x)+x=\sqrt {a^2+x^2}\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 396 |
\(\sqrt {b^2+x^2} y'(x)=\sqrt {a^2+y(x)^2}\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 397 |
\(\sqrt {b^2-x^2} y'(x)=\sqrt {a^2-y(x)^2}\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 398 |
\(x \sqrt {a^2+x^2} y'(x)=y(x) \sqrt {b^2+y(x)^2}\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 399 |
\(x \sqrt {x^2-a^2} y'(x)=y(x) \sqrt {y(x)^2-b^2}\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 400 |
\(\sqrt {X} y'(x)+\sqrt {Y}=0\) [_quadrature] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 401 |
\(\sqrt {X} y'(x)=\sqrt {Y}\) [_quadrature] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 402 |
\(x^{3/2} y'(x)=a+b x^{3/2} y(x)^2\) [_rational, [_Riccati, _special]] Solution method Abel ODE, First kind Maple ✓ |
| ODE 403 |
\(\sqrt {x^3+1} y'(x)=\sqrt {y(x)^3+1}\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 404 |
\(\sqrt {(1-x) x (1-a x)} y'(x)=\sqrt {(1-y(x)) y(x) (1-a y(x))}\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 405 |
\(\sqrt {1-x^4} y'(x)=\sqrt {1-y(x)^4}\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 406 |
\(\sqrt {x^4+x^2+1} y'(x)=\sqrt {y(x)^4+y(x)^2+1}\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 407 |
\(\sqrt {X} y'(x)=0\) [_quadrature] Solution method Separable ODE, Dependent variable missing Maple ✓ |
| ODE 408 |
\(\sqrt {X} y'(x)+\sqrt {Y}=0\) [_quadrature] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 409 |
\(\sqrt {X} y'(x)=\sqrt {Y}\) [_quadrature] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 410 |
\(\left (x^3+1\right )^{2/3} y'(x)+\left (y(x)^3+1\right )^{2/3}=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 411 |
\(\left (\text {a0}+\text {a1} x+4 x^3\right )^{2/3} y'(x)+\left (\text {a0}+\text {a1} y(x)+4 y(x)^3\right )^{2/3}=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 412 |
\(X^{2/3} y'(x)=Y^{2/3}\) [_quadrature] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 413 |
\(\left (a+\cos ^2\left (\frac {x}{2}\right )\right ) y'(x)=y(x) \tan \left (\frac {x}{2}\right ) \left (a-y(x)+\cos ^2\left (\frac {x}{2}\right )+1\right )\) [_Bernoulli] Solution method Change of Variable, Two new variables Maple ✓ |
| ODE 414 |
\(\left (1-4 \cos ^2(x)\right ) y'(x)=y(x) \left (4 \cos ^2(x)+1\right ) \tan (x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 415 |
\((1-\sin (x)) y'(x)+y(x) \cos (x)=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 416 |
\(y'(x) (\cos (x)-\sin (x))+y(x) (\sin (x)+\cos (x))=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 417 |
\(y'(x) \left (\text {a0}+\text {a1} \sin ^2(x)\right )+\text {a2} x \left (\text {a1} \sin ^2(x)+\text {a3}\right )+\text {a1} y(x) \sin (2 x)=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 418 |
\(\left (x-e^x\right ) y'(x)+\left (1-e^x\right ) y(x)+e^x x=0\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 419 |
\(x \log (x) y'(x)=a x (\log (x)+1)-y(x)\) [_linear] Solution method Linear ODE Maple ✓ |
| ODE 420 |
\(y(x) y'(x)+x=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 421 |
\(e^{x^2} x+y(x) y'(x)=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 422 |
\(x^3+y(x) y'(x)+y(x)=0\) [_rational, [_Abel, `2nd type`, `class A`]] Solution method Abel ODE, Second kind Maple ✗ |
| ODE 423 |
\(a x+b y(x)+y(x) y'(x)=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Homogeneous equation Maple ✓ |
| ODE 424 |
\(y(x) y'(x)+e^{-x} x (y(x)+1)=0\) [_separable] Solution method Linear ODE Maple ✓ |
| ODE 425 |
\(f(x)+y(x) y'(x)=g(x) y(x)\) [[_Abel, `2nd type`, `class A`]] Solution method Exact equation, integrating factor Maple ✗ |
| ODE 426 |
\(y(x) y'(x)+y(x)^2+4 x (x+1)=0\) [[_homogeneous, `class D`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 427 |
\(y(x) y'(x)=a x+b y(x)^2\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 428 |
\(y(x) y'(x)=a y(x)^2+b \cos (c+x)\) [_Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 429 |
\(y(x) y'(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2\) [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 430 |
\(y(x) y'(x)=a x+b x y(x)^2\) [_separable] Solution method The Bernoulli ODE Maple ✓ |
| ODE 431 |
\(y(x) y'(x)=\csc ^2(x)-y(x)^2 \cot (x)\) [_Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 432 |
\(y(x) y'(x)=\sqrt {a^2+y(x)^2}\) [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 433 |
\(y(x) y'(x)=\sqrt {y(x)^2-a^2}\) [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 434 |
\(g(x) f\left (x^2+y(x)^2\right )+y(x) y'(x)+x=0\) [NONE] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 435 |
\((y(x)+1) y'(x)=y(x)+x\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 436 |
\((y(x)+1) y'(x)=x^2 (1-y(x))\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 437 |
\((y(x)+x) y'(x)+y(x)=0\) [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]] Solution method Homogeneous equation Maple ✓ |
| ODE 438 |
\((x-y(x)) y'(x)=y(x)\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Homogeneous equation Maple ✓ |
| ODE 439 |
\((y(x)+x) y'(x)-y(x)+x=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Homogeneous equation Maple ✓ |
| ODE 440 |
\((y(x)+x) y'(x)=x-y(x)\) [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]] Solution method Homogeneous equation Maple ✓ |
| ODE 441 |
\(1-y'(x)=y(x)+x\) [[_linear, `class A`]] Solution method Homogeneous equation Maple ✓ |
| ODE 442 |
\((x-y(x)) y'(x)=y(x) (2 x y(x)+1)\) [[_homogeneous, `class D`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 443 |
\((y(x)+x) y'(x)+\tan (y(x))=0\) [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 444 |
\((x-y(x)) y'(x)=\left (e^{-\frac {x}{y(x)}}+1\right ) y(x)\) [[_homogeneous, `class A`], _dAlembert] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 445 |
\((y(x)+x+1) y'(x)+3 y(x)+4 x+1=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 446 |
\((y(x)+x+2) y'(x)=-y(x)-x+1\) [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 447 |
\((-y(x)-x+3) y'(x)=-3 y(x)+x+1\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 448 |
\((y(x)-x+3) y'(x)=3 y(x)-4 x+11\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 449 |
\((y(x)+2 x) y'(x)-2 y(x)+x=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Homogeneous equation Maple ✓ |
| ODE 450 |
\((-y(x)+2 x+2) y'(x)+3 (-y(x)+2 x+1)=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 451 |
\((-y(x)+2 x+3) y'(x)+2=0\) [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 452 |
\((-y(x)+2 x+4) y'(x)-2 y(x)+x+5=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 453 |
\((-y(x)-2 x+5) y'(x)-2 y(x)-x+4=0\) [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 454 |
\((y(x)-3 x+1) y'(x)=2 (x-y(x))\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 455 |
\((y(x)-3 x+2) y'(x)-3 y(x)-2 x+5=0\) [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 456 |
\((4 x-y(x)) y'(x)-5 y(x)+2 x=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 457 |
\((-y(x)-4 x+6) y'(x)=2 x-y(x)\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 458 |
\((-y(x)+5 x+1) y'(x)-5 y(x)+x+5=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 459 |
\(y'(x) (a+b x+y(x))+a-b x-y(x)=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 460 |
\(\left (x^2-y(x)\right ) y'(x)+x=0\) [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]] Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 461 |
\(\left (x^2-y(x)\right ) y'(x)=4 x y(x)\) [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 462 |
\(y'(x) (y(x)-\cot (x) \csc (x))+y(x) \csc (x) (y(x) \cos (x)+1)=0\) [[_Abel, `2nd type`, `class A`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 463 |
\(x^2+2 y(x) y'(x)+y(x)^2+2 x=0\) [[_homogeneous, `class D`], _rational, _Bernoulli] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 464 |
\(2 y(x) y'(x)=x^3+x y(x)^2\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 465 |
\((x-2 y(x)) y'(x)=y(x)\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 466 |
\((2 y(x)+x) y'(x)-y(x)+2 x=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Homogeneous equation Maple ✓ |
| ODE 467 |
\((x-2 y(x)) y'(x)+y(x)+2 x=0\) [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]] Solution method Exact equation Maple ✓ |
| ODE 468 |
\((-2 y(x)+x+1) y'(x)=-y(x)+2 x+1\) [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]] Solution method Exact equation Maple ✓ |
| ODE 469 |
\((2 y(x)+x+1) y'(x)-2 y(x)-x+1=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 470 |
\((2 y(x)+x+1) y'(x)-4 y(x)+x+7=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 471 |
\(x^2+2 (y(x)+x) y'(x)+2 y(x)=0\) [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]] Solution method Exact equation Maple ✓ |
| ODE 472 |
\((-2 y(x)+2 x+3) y'(x)=-2 y(x)+6 x+1\) [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 473 |
\((-2 y(x)-4 x+1) y'(x)+y(x)+2 x=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 474 |
\((6 x-2 y(x)) y'(x)=-y(x)+3 x+2\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 475 |
\((2 y(x)+9 x+19) y'(x)-6 y(x)-2 x+18=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 476 |
\(\left (x^3+2 y(x)\right ) y'(x)=3 x (2-x y(x))\) [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]] Solution method Exact equation Maple ✓ |
| ODE 477 |
\(y'(x) (\tan (x) \sec (x)-2 y(x))+\sec (x) (2 y(x) \sin (x)+1)=0\) [[_Abel, `2nd type`, `class A`]] Solution method Exact equation, integrating factor Maple ✗ |
| ODE 478 |
\(\left (e^{-x} x-2 y(x)\right ) y'(x)=2 e^{-2 x} x-\left (-2 y(x)+e^{-x} x+e^{-x}\right ) y(x)\) [[_Abel, `2nd type`, `class B`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 479 |
\(3 y(x) y'(x)+5 \cot (x) \cos ^2(y(x)) \cot (y(x))=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 480 |
\(3 (2-y(x)) y'(x)+x y(x)=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 481 |
\((x-3 y(x)) y'(x)-y(x)+3 x+4=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 482 |
\((-3 y(x)-x+4) y'(x)-3 y(x)-x+3=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 483 |
\((3 y(x)+2 x+2) y'(x)=-3 y(x)-2 x+1\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 484 |
\((-3 y(x)-2 x+5) y'(x)-3 y(x)-2 x+1=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 485 |
\((-3 y(x)+9 x+1) y'(x)-y(x)+3 x+2=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 486 |
\((4 y(x)+x) y'(x)-y(x)+4 x=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 487 |
\((4 y(x)+2 x+3) y'(x)=2 y(x)+x+1\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 488 |
\((-4 y(x)+2 x+5) y'(x)=-2 y(x)+x+3\) [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 489 |
\((-4 y(x)+3 x+5) y'(x)=-3 y(x)+7 x+2\) [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 490 |
\(4 (-y(x)-x+1) y'(x)-x+2=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 491 |
\((-4 y(x)-11 x+11) y'(x)=-25 y(x)-8 x+62\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 492 |
\((5 y(x)+3 x+6) y'(x)=7 y(x)+x+2\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 493 |
\((5 y(x)+7 x) y'(x)+8 y(x)+10 x=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Homogeneous equation Maple ✓ |
| ODE 494 |
\(\left (4 x^3+5 y(x)+x\right ) y'(x)+7 x^3+3 x^2 y(x)+4 y(x)=0\) [_rational, [_Abel, `2nd type`, `class A`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 495 |
\((6 y(x)-x+5) y'(x)=4 y(x)-x+3\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 496 |
\(3 (2 y(x)+x) y'(x)=-2 y(x)-x+1\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 497 |
\((7 y(x)-3 x+3) y'(x)+3 y(x)-7 x+7=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 498 |
\((9 y(x)+x+1) y'(x)+5 y(x)+x+1=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 499 |
\((-12 y(x)+5 x+8) y'(x)=-5 y(x)+2 x+3\) [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 500 |
\((-16 y(x)+7 x+140) y'(x)+y(x)+8 x+25=0\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 501 |
\((21 y(x)+9 x+3) y'(x)=-5 y(x)+7 x+45\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 502 |
\(y'(x) (a x+b y(x))+x=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert] Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 503 |
\(y'(x) (a x+b y(x))+y(x)=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 504 |
\(y'(x) (a x+b y(x))+a y(x)+b x=0\) [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]] Solution method Exact equation Maple ✓ |
| ODE 505 |
\(y'(x) (a x+b y(x))=a y(x)+b x\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 506 |
\(\text {a1}+y'(x) (\text {a2}+b x+\text {c2} y(x))+b y(x)+\text {b1} x=0\) [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 507 |
\(y'(x) (\text {a2}+\text {b2} y(x)+\text {c2} y(x))=\text {a1}+\text {b1} x+\text {c1} y(x)\) [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 508 |
\(x y(x) y'(x)+y(x)^2+1=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 509 |
\(x y(x) y'(x)=y(x)^2+x\) [[_homogeneous, `class D`], _rational, _Bernoulli] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 510 |
\(x^2+x y(x) y'(x)+y(x)^2=0\) [[_homogeneous, `class A`], _rational, _Bernoulli] Solution method Homogeneous equation Maple ✓ |
| ODE 511 |
\(x^4+x y(x) y'(x)-y(x)^2=0\) [[_homogeneous, `class D`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 512 |
\(x y(x) y'(x)=a x^3 \cos (x)+y(x)^2\) [[_homogeneous, `class D`], _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 513 |
\(x y(x) y'(x)=x^2-x y(x)+y(x)^2\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation Maple ✓ |
| ODE 514 |
\(2 x^2+x y(x) y'(x)-2 x y(x)-y(x)^2=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation Maple ✓ |
| ODE 515 |
\(x y(x) y'(x)=a+b y(x)^2\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 516 |
\(x y(x) y'(x)=a x^n+b y(x)^2\) [[_homogeneous, `class G`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 517 |
\(x y(x) y'(x)=\left (x^2+1\right ) \left (1-y(x)^2\right )\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 518 |
\(x^2 \cot ^{-1}\left (\frac {y(x)}{x}\right )+x y(x) y'(x)-y(x)^2=0\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 519 |
\(x^2 e^{-\frac {2 y(x)}{x}}+x y(x) y'(x)-y(x)^2=0\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 520 |
\((x y(x)+1) y'(x)+y(x)^2=0\) [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 521 |
\(x (y(x)+1) y'(x)-(1-x) y(x)=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 522 |
\(x (1-y(x)) y'(x)+(x+1) y(x)=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 523 |
\(x (1-y(x)) y'(x)+(1-x) y(x)=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 524 |
\(a x+x (y(x)+2) y'(x)=0\) [_quadrature] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 525 |
\((x (-y(x))+3 x+2) y'(x)+y(x)=0\) [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]] Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 526 |
\(x (y(x)+4) y'(x)=y(x)^2+2 y(x)+2 x\) [_rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation, special Maple ✓ |
| ODE 527 |
\(x (a+y(x)) y'(x)+b x+c y(x)=0\) [_rational, [_Abel, `2nd type`, `class B`]] Solution method Change of Variable, new independent variable Maple ✗ |
| ODE 528 |
\(x (a+y(x)) y'(x)=y(x) (A+B x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 529 |
\(x (y(x)+x) y'(x)+y(x)^2=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation Maple ✓ |
| ODE 530 |
\(x (x-y(x)) y'(x)+y(x)^2=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation Maple ✓ |
| ODE 531 |
\(x (y(x)+x) y'(x)=x^2+y(x)^2\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation Maple ✓ |
| ODE 532 |
\(2 x^2+x (x-y(x)) y'(x)+3 x y(x)-y(x)^2=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 533 |
\(x \sqrt {x^2-y(x)^2}+x (y(x)+x) y'(x)-y(x) (y(x)+x)=0\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 534 |
\((a+x (y(x)+x)) y'(x)=b y(x) (y(x)+x)\) [_rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation, special Maple ✗ |
| ODE 535 |
\(x (y(x)+2 x) y'(x)=x^2+x y(x)-y(x)^2\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation Maple ✓ |
| ODE 536 |
\(4 x^2+x (4 x-y(x)) y'(x)-6 x y(x)-y(x)^2=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation Maple ✓ |
| ODE 537 |
\(x \left (x^3+y(x)\right ) y'(x)=\left (x^3-y(x)\right ) y(x)\) [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 538 |
\(x \left (2 x^3+y(x)\right ) y'(x)=\left (2 x^3-y(x)\right ) y(x)\) [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 539 |
\(x \left (2 x^3+y(x)\right ) y'(x)=6 y(x)^2\) [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 540 |
\((1-x) y(x) y'(x)+x (1-y(x))=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 541 |
\((a+x) (b+x) y'(x)=x y(x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 542 |
\(-2 x^3+2 x y(x) y'(x)-y(x)^2+1=0\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 543 |
\(a+2 x y(x) y'(x)+y(x)^2=0\) [_separable] Solution method Exact equation Maple ✓ |
| ODE 544 |
\(2 x y(x) y'(x)=a x+y(x)^2\) [[_homogeneous, `class G`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 545 |
\(x^2+2 x y(x) y'(x)+y(x)^2=0\) [[_homogeneous, `class A`], _exact, _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 546 |
\(2 x y(x) y'(x)=x^2+y(x)^2\) [[_homogeneous, `class A`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 547 |
\(2 x y(x) y'(x)=4 (2 x+1) x^2+y(x)^2\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 548 |
\(x^2 \left (a x^3+1\right )+2 x y(x) y'(x)=6 y(x)^2\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 549 |
\(3 x^2+(2 x y(x)-x+3) y'(x)+y(x)^2-y(x)=0\) [_exact, _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation Maple ✓ |
| ODE 550 |
\(x (x-2 y(x)) y'(x)+y(x)^2=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation Maple ✓ |
| ODE 551 |
\(x (2 y(x)+x) y'(x)+(2 x-y(x)) y(x)=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation Maple ✓ |
| ODE 552 |
\(x (x-2 y(x)) y'(x)+(2 x-y(x)) y(x)=0\) [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation Maple ✓ |
| ODE 553 |
\(x (-2 y(x)+x+1) y'(x)+y(x) (y(x)-2 x+1)=0\) [_rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 554 |
\(x (-2 y(x)-x+1) y'(x)+y(x) (y(x)+2 x+1)=0\) [_rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 555 |
\(2 x \left (2 x^2+y(x)\right ) y'(x)+y(x) \left (12 x^2+y(x)\right )=0\) [[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation Maple ✓ |
| ODE 556 |
\(-3 x^2+2 (x+1) y(x) y'(x)+y(x)^2+2 x=0\) [_exact, _rational, _Bernoulli] Solution method Exact equation Maple ✓ |
| ODE 557 |
\(x (3 y(x)+2 x) y'(x)=y(x)^2\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation Maple ✓ |
| ODE 558 |
\(x (3 y(x)+2 x) y'(x)+3 (y(x)+x)^2=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 559 |
\(\left (x^2+6 x y(x)+3\right ) y'(x)+3 y(x)^2+2 x y(x)+2 x=0\) [_exact, _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation Maple ✓ |
| ODE 560 |
\(x^3+3 x (2 y(x)+x) y'(x)+3 y(x) (y(x)+2 x)=0\) [_exact, _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation Maple ✓ |
| ODE 561 |
\(a x y(x) y'(x)=x^2+y(x)^2\) [[_homogeneous, `class A`], _rational, _Bernoulli] Solution method Homogeneous equation Maple ✓ |
| ODE 562 |
\(a x y(x) y'(x)+x^2-y(x)^2=0\) [[_homogeneous, `class A`], _rational, _Bernoulli] Solution method Homogeneous equation Maple ✓ |
| ODE 563 |
\(x y'(x) (a+b y(x))=c y(x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 564 |
\(x (x-a y(x)) y'(x)=y(x) (y(x)-a x)\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation Maple ✓ |
| ODE 565 |
\(y'(x) (x (A x+B y(x))+\text {a0}+\text {a1} x+\text {a2} y(x))=y(x) (A x+B y(x))+\text {b0}+\text {b1} x+\text {b2} y(x)\) [_rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation, Jacobi equation Maple ✓ |
| ODE 566 |
\(y'(x) (x (\text {a1}+\text {b2} x+\text {c2} y(x))+\text {a1}+\text {b1} x+\text {c1} y(x))=y(x) (\text {a2}+\text {b2} x+\text {c2} y(x))+\text {a3}+\text {b3} x+\text {c2} y(x)\) [_rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation, Jacobi equation Maple ✓ |
| ODE 567 |
\(x y'(x) \left (a y(x)+x^n\right )+y(x)^2 (b+c y(x))=0\) [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 568 |
\(\left (1-x^2 y(x)\right ) y'(x)-x y(x)^2+1=0\) [_exact, _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation Maple ✓ |
| ODE 569 |
\(\left (1-x^2 y(x)\right ) y'(x)+x y(x)^2-1=0\) [_rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation, special Maple ✓ |
| ODE 570 |
\(x (1-x y(x)) y'(x)+y(x) (x y(x)+1)=0\) [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 571 |
\(x (x y(x)+2) y'(x)=2 x^3-x y(x)^2-2 y(x)+3\) [_exact, _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation Maple ✓ |
| ODE 572 |
\(x (2-x y(x)) y'(x)-x (x y(x)+1) y(x)^2+2 y(x)=0\) [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class C`]] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 573 |
\(x (3-x y(x)) y'(x)=y(x) (x y(x)-1)\) [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 574 |
\(x^2 (1-y(x)) y'(x)+(1-x) y(x)=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 575 |
\(x^2 (1-y(x)) y'(x)+(x+1) y(x)^2=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 576 |
\(\left (x^2+1\right ) y(x) y'(x)+x \left (1-y(x)^2\right )=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 577 |
\(\left (1-x^2\right ) y(x) y'(x)+2 x^2+x y(x)^2=0\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 578 |
\(2 x^2 y(x) y'(x)=x^2 (2 x+1)-y(x)^2\) [[_homogeneous, `class D`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 579 |
\(x (1-2 x y(x)) y'(x)+y(x) (2 x y(x)+1)=0\) [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Change of Variable, Two new variables Maple ✓ |
| ODE 580 |
\(x (2 x y(x)+1) y'(x)+y(x) (3 x y(x)+2)=0\) [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Homogeneous equation, isobaric equation Maple ✓ |
| ODE 581 |
\(y(x) \left (-x^2 y(x)^2+2 x y(x)+1\right )+x (2 x y(x)+1) y'(x)=0\) [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class C`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 582 |
\(x^2 (x-2 y(x)) y'(x)=2 x^3-4 x y(x)^2+y(x)^3\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 583 |
\(2 x (x+1) y(x) y'(x)=y(x)^2+1\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 584 |
\(3 x^2 y(x) y'(x)+2 x y(x)^2+1=0\) [[_homogeneous, `class G`], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 585 |
\(x^2 (4 x-3 y(x)) y'(x)=y(x) \left (6 x^2-3 x y(x)+2 y(x)^2\right )\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 586 |
\(\left (1-x^3 y(x)\right ) y'(x)=x^2 y(x)^2\) [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 587 |
\(a+2 x^3 y(x) y'(x)+3 x^2 y(x)^2=0\) [[_homogeneous, `class G`], _exact, _rational, _Bernoulli] Solution method Exact equation Maple ✓ |
| ODE 588 |
\(x \left (3-2 x^2 y(x)\right ) y'(x)=3 x^2 y(x)^2-3 y(x)+4 x\) [_exact, _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation Maple ✓ |
| ODE 589 |
\(x \left (2 x^2 y(x)+3\right ) y'(x)+y(x) \left (3 x^2 y(x)+4\right )=0\) [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 590 |
\(3 x^4+8 x^3 y(x) y'(x)-6 x^2 y(x)^2-y(x)^4=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 591 |
\(x y(x) \left (a+b x^2\right ) y'(x)=A+B y(x)^2\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 592 |
\(3 x^4 y(x) y'(x)=1-2 x^3 y(x)^2\) [[_homogeneous, `class G`], _rational, _Bernoulli] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 593 |
\(x^7 y(x) y'(x)=5 x^3 y(x)+2 \left (x^2+1\right )\) [_rational, [_Abel, `2nd type`, `class B`]] Solution method Abel ODE, Second kind Maple ✓ |
| ODE 594 |
\(\sqrt {x^2+1} y(x) y'(x)+x \sqrt {y(x)^2+1}=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 595 |
\(\sqrt {x^2+1} (y(x)+1) y'(x)=y(x)^3\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 596 |
\(y'(x) (\text {g0}(x)+\text {g1}(x) y(x))=\text {f0}(x)+\text {f1}(x) y(x)+\text {f2}(x) y(x)^2+\text {f3}(x) y(x)^3\) [[_Abel, `2nd type`, `class C`]] Solution method Abel ODE, Second kind Maple ✗ |
| ODE 597 |
\(y(x)^2 y'(x)+x (2-y(x))=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 598 |
\(y(x)^2 y'(x)=x \left (y(x)^2+1\right )\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 599 |
\(\left (y(x)^2+x\right ) y'(x)+y(x)=a+b x\) [_exact, _rational] Solution method Exact equation Maple ✓ |
| ODE 600 |
\(\left (x-y(x)^2\right ) y'(x)=x^2-y(x)\) [_exact, _rational] Solution method Exact equation Maple ✓ |
| ODE 601 |
\(\left (x^2+y(x)^2\right ) y'(x)+x y(x)=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 602 |
\(\left (x^2+y(x)^2\right ) y'(x)=x y(x)\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 603 |
\(\left (x^2-y(x)^2\right ) y'(x)=2 x y(x)\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 604 |
\(\left (x^2-y(x)^2\right ) y'(x)+x (2 y(x)+x)=0\) [[_homogeneous, `class A`], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓ |
| ODE 605 |
\(\left (x^2+y(x)^2\right ) y'(x)+2 x (y(x)+2 x)=0\) [[_homogeneous, `class A`], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓ |
| ODE 606 |
\(\left (-x^2+y(x)^2+1\right ) y'(x)=x^2-y(x)^2+1\) [[_1st_order, _with_linear_symmetries], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 607 |
\(\left (a^2+x^2+y(x)^2\right ) y'(x)+2 x y(x)=0\) [_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]] Solution method Exact equation Maple ✓ |
| ODE 608 |
\(\left (a^2+x^2+y(x)^2\right ) y'(x)+b^2+x^2+2 x y(x)=0\) [_exact, _rational] Solution method Exact equation Maple ✓ |
| ODE 609 |
\(\left (x^2+y(x)^2+x\right ) y'(x)=y(x)\) [_rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 610 |
\(\left (3 x^2-y(x)^2\right ) y'(x)=2 x y(x)\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 611 |
\(\left (x^4+y(x)^2\right ) y'(x)=4 x^3 y(x)\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 612 |
\(y(x) (y(x)+1) y'(x)=x (x+1)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 613 |
\(\left (y(x)^2+2 y(x)+x\right ) y'(x)+y(x)^2 (y(x)+x)^2+y(x) (y(x)+1)=0\) [_rational] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 614 |
\(\left (x^2+y(x)^2+2 y(x)\right ) y'(x)+2 x=0\) [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 615 |
\(\left (x^3-y(x)^2+2 y(x)\right ) y'(x)+3 x^2 y(x)=0\) [_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]] Solution method Exact equation Maple ✓ |
| ODE 616 |
\(\left (y(x)^2+x y(x)+y(x)+1\right ) y'(x)+y(x)+1=0\) [[_1st_order, _with_linear_symmetries], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 617 |
\((y(x)+x)^2 y'(x)=a^2\) [[_homogeneous, `class C`], _dAlembert] Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\) Maple ✓ |
| ODE 618 |
\((x-y(x))^2 y'(x)=a^2\) [[_homogeneous, `class C`], _dAlembert] Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\) Maple ✓ |
| ODE 619 |
\(\left (x^2+2 x y(x)-y(x)^2\right ) y'(x)+x^2-2 x y(x)+y(x)^2=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 620 |
\((x-y(x))^2 y'(x)=(-y(x)+x+1)^2\) [[_homogeneous, `class C`], _rational, _dAlembert] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 621 |
\((y(x)+x)^2 y'(x)=(y(x)+x+2)^2\) [[_homogeneous, `class C`], _rational, _dAlembert] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 622 |
\((y(x)+x)^2 y'(x)=x^2-2 x y(x)+5 y(x)^2\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 623 |
\(y'(x) (a+b+y(x)+x)^2=2 (a+y(x))^2\) [[_homogeneous, `class C`], _rational] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 624 |
\(\left (2 x^2+4 x y(x)-y(x)^2\right ) y'(x)=x^2-4 x y(x)-2 y(x)^2\) [[_homogeneous, `class A`], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓ |
| ODE 625 |
\((y(x)+3 x)^2 y'(x)=4 y(x) (2 y(x)+3 x)\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 626 |
\((-y(x)-3 x+1)^2 y'(x)=(-4 y(x)-6 x+3) (1-2 y(x))\) [[_homogeneous, `class C`], _rational] Solution method Change of Variable, Two new variables Maple ✓ |
| ODE 627 |
\(y'(x) \left (\cot (x)-2 y(x)^2\right )=y(x)^3 \csc (x) \sec (x)\) [`y=_G(x,y')`] Solution method Change of Variable, new independent variable Maple ✗ |
| ODE 628 |
\(3 y(x)^2 y'(x)=a y(x)^3+x+1\) [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 629 |
\(\left (x^2-3 y(x)^2\right ) y'(x)+2 x y(x)+1=0\) [_exact, _rational] Solution method Exact equation Maple ✓ |
| ODE 630 |
\(\left (2 x^2+3 y(x)^2\right ) y'(x)+x (y(x)+3 x)=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Exact equation Maple ✓ |
| ODE 631 |
\(3 \left (x^2-y(x)^2\right ) y'(x)-2 y(x)^3+6 x (x+1) y(x)+3 e^x=0\) [`y=_G(x,y')`] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 632 |
\(\left (3 x^2+2 x y(x)+4 y(x)^2\right ) y'(x)+2 x^2+6 x y(x)+y(x)^2=0\) [[_homogeneous, `class A`], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓ |
| ODE 633 |
\((2 y(x)-3 x+1)^2 y'(x)=(-3 y(x)+2 x+4)^2\) [[_homogeneous, `class C`], _rational] Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 634 |
\(\left (-3 x^2 y(x)+6 y(x)^2+1\right ) y'(x)+x^2-3 x y(x)^2=0\) [_exact, _rational] Solution method Exact equation Maple ✓ |
| ODE 635 |
\(a+(x-6 y(x))^2 y'(x)-6 y(x)^2+2 x y(x)=0\) [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`]] Solution method Exact equation Maple ✓ |
| ODE 636 |
\(\left (a y(x)^2+x^2\right ) y'(x)=x y(x)\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 637 |
\(\left (a y(x)^2+x^2+x y(x)\right ) y'(x)=a x^2+x y(x)+y(x)^2\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 638 |
\(\left (a x^2-a y(x)^2+2 x y(x)\right ) y'(x)-2 a x y(x)+x^2-y(x)^2=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 639 |
\(y'(x) \left (x^2 (a+2 b)+2 x (2 b+c) y(x)+3 c y(x)^2\right )+2 x (a+2 b) y(x)+3 a x^2+(2 b+c) y(x)^2=0\) [[_homogeneous, `class A`], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓ |
| ODE 640 |
\(y'(x) \left (a x^2+2 b x y(x)+c y(x)^2\right )+2 a x y(x)+b y(x)^2+k x^2=0\) [[_homogeneous, `class A`], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓ |
| ODE 641 |
\(x \left (1-y(x)^2\right ) y'(x)=\left (x^2+1\right ) y(x)\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 642 |
\(x \left (3 x-y(x)^2\right ) y'(x)+y(x) \left (5 x-2 y(x)^2\right )=0\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 643 |
\(x \left (x^2+y(x)^2\right ) y'(x)=y(x) \left (x^4+x^2+y(x)^2\right )\) [[_homogeneous, `class D`], _rational] Solution method Homogeneous equation, \(xy'(x)=x f(x) g(u)+y(x)\) Maple ✓ |
| ODE 644 |
\(x \left (-x^2+y(x)^2+1\right ) y'(x)+y(x) \left (x^2-y(x)^2+1\right )=0\) [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Homogeneous equation, special Maple ✓ |
| ODE 645 |
\(x \left (a-x^2-y(x)^2\right ) y'(x)+y(x) \left (a+x^2+y(x)^2\right )=0\) [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Homogeneous equation, special Maple ✓ |
| ODE 646 |
\(x \left (2 x^2+y(x)^2\right ) y'(x)=y(x) \left (2 x^2+3 y(x)^2\right )\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 647 |
\(\left (x \left (a-x^2-y(x)^2\right )+y(x)\right ) y'(x)-y(x) \left (a-x^2-y(x)^2\right )+x=0\) [[_1st_order, _with_linear_symmetries], _rational] Solution method Change of Variable, Two new variables Maple ✓ |
| ODE 648 |
\(x (a+y(x))^2 y'(x)=b y(x)^2\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 649 |
\(x \left (x^2-x y(x)+y(x)^2\right ) y'(x)+y(x) \left (x^2+x y(x)+y(x)^2\right )=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 650 |
\(x \left (x^2-x y(x)-y(x)^2\right ) y'(x)=y(x) \left (x^2+x y(x)-y(x)^2\right )\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 651 |
\(x \left (a x y(x)+x^2+y(x)^2\right ) y'(x)=y(x) \left (b x y(x)+x^2+y(x)^2\right )\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 652 |
\(x \left (x^2-2 y(x)^2\right ) y'(x)=y(x) \left (2 x^2-y(x)^2\right )\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 653 |
\(x \left (x^2+2 y(x)^2\right ) y'(x)=y(x) \left (2 x^2+3 y(x)^2\right )\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 654 |
\(2 x \left (5 x^2+y(x)^2\right ) y'(x)=x^2 y(x)-y(x)^3\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 655 |
\(x \left (a x y(x)+x^2+2 y(x)^2\right ) y'(x)=y(x)^2 (a x+2 y(x))\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 656 |
\(3 x y(x)^2 y'(x)=2 x-y(x)^3\) [[_homogeneous, `class G`], _exact, _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 657 |
\(\left (3 x y(x)^2-4 x+1\right ) y'(x)=y(x) \left (2-y(x)^2\right )\) [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 658 |
\(x \left (x-3 y(x)^2\right ) y'(x)+y(x) \left (2 x-y(x)^2\right )=0\) [[_homogeneous, `class G`], _exact, _rational] Solution method Exact equation Maple ✓ |
| ODE 659 |
\(x^3+3 x \left (y(x)^2+x\right ) y'(x)-3 x y(x)-2 y(x)^3=0\) [_rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 660 |
\(x \left (-3 x^3 y(x)+x^3+4 y(x)^2\right ) y'(x)=6 y(x)^3\) [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]] Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 661 |
\(6 x y(x)^2 y'(x)+2 y(x)^3+x=0\) [[_homogeneous, `class G`], _exact, _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 662 |
\(x \left (6 y(x)^2+x\right ) y'(x)-3 y(x)^3+x y(x)=0\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 663 |
\(x \left (x^2-6 y(x)^2\right ) y'(x)=4 y(x) \left (x^2+3 y(x)^2\right )\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 664 |
\(x \left (3 x-7 y(x)^2\right ) y'(x)+y(x) \left (5 x-3 y(x)^2\right )=0\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 665 |
\(x^3+x^2 y(x)^2 y'(x)-x+1=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 666 |
\(\left (1-x^2 y(x)^2\right ) y'(x)=x y(x)^3\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 667 |
\(\left (1-x^2 y(x)^2\right ) y'(x)=y(x)^2 (x y(x)+1)\) [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 668 |
\(x \left (x y(x)^2+1\right ) y'(x)+y(x)=0\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 669 |
\(x \left (x y(x)^2+1\right ) y'(x)=y(x) \left (2-3 x y(x)^2\right )\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 670 |
\(x^2 (a+y(x))^2 y'(x)=\left (x^2+1\right ) \left (a^2+y(x)^2\right )\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 671 |
\(\left (x^2+1\right ) \left (y(x)^2+1\right ) y'(x)+2 x y(x) \left (1-y(x)^2\right )=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 672 |
\(\left (x^2+1\right ) \left (y(x)^2+1\right ) y'(x)+2 x y(x) (1-y(x))^2=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 673 |
\(\left (-x^3+6 x^2 y(x)^2+1\right ) y'(x)=x \left (-4 y(x)^3+3 x y(x)+6\right )\) [_exact, _rational] Solution method Exact equation Maple ✓ |
| ODE 674 |
\(x \left (4 x^2 y(x)-12 x y(x)^2+5 x+3\right ) y'(x)+y(x) \left (6 x^2 y(x)-8 x y(x)^2+10 x+3\right )=0\) [_exact, _rational] Solution method Exact equation Maple ✓ |
| ODE 675 |
\(x^3 \left (y(x)^2+1\right ) y'(x)+3 x^2 y(x)=0\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 676 |
\(y(x) \left (x^2 y(x)^2+1\right )+x (1-x y(x))^2 y'(x)=0\) [[_homogeneous, `class G`], _rational] Solution method Homogeneous equation, isobaric equation Maple ✓ |
| ODE 677 |
\(\left (1-x^4 y(x)^2\right ) y'(x)=x^3 y(x)^3\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 678 |
\(\left (3 x-y(x)^3\right ) y'(x)=x^2-3 y(x)\) [_exact, _rational] Solution method Exact equation Maple ✓ |
| ODE 679 |
\(\left (x^3-y(x)^3\right ) y'(x)+x^2 y(x)=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 680 |
\(x^2 (a x+3 y(x))+\left (x^3+y(x)^3\right ) y'(x)=0\) [[_homogeneous, `class A`], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓ |
| ODE 681 |
\(\left (-x^2 y(x)-y(x)^3+x\right ) y'(x)=x^3+x y(x)^2-y(x)\) [_exact, _rational] Solution method Exact equation Maple ✓ |
| ODE 682 |
\(\left (a^2 x+y(x) \left (x^2-y(x)^2\right )\right ) y'(x)+x \left (x^2-y(x)^2\right )=a^2 y(x)\) [_rational] Solution method Change of Variable, Two new variables Maple ✗ |
| ODE 683 |
\(y(x) \left (a+x^2+y(x)^2\right ) y'(x)=x \left (a-x^2-y(x)^2\right )\) [_exact, _rational] Solution method Exact equation Maple ✓ |
| ODE 684 |
\(y(x) \left (3 x^2+y(x)^2\right ) y'(x)+x \left (x^2+3 y(x)^2\right )=0\) [[_homogeneous, `class A`], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓ |
| ODE 685 |
\(y(x) \left (a-3 x^2-y(x)^2\right ) y'(x)+x \left (a-x^2+y(x)^2\right )=0\) [_rational] Solution method Change of Variable, Two new variables Maple ✓ |
| ODE 686 |
\(2 y(x)^3 y'(x)=x^3-x y(x)^2\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 687 |
\(y(x) \left (2 y(x)^2+1\right ) y'(x)=x \left (2 x^2+1\right )\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 688 |
\(x^3+y(x) \left (3 x^2+2 y(x)^2\right ) y'(x)=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 689 |
\(y(x) \left (5 x^2+2 y(x)^2\right ) y'(x)+x \left (x^2+5 y(x)^2\right )=0\) [[_homogeneous, `class A`], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓ |
| ODE 690 |
\(2 x^3+3 x^2 y(x)+\left (-x^3+x^2+3 x y(x)^2+2 y(x)^3\right ) y'(x)-y(x)^3+y(x)^2=0\) [_rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 691 |
\(4 x^3+9 x^2 y(x)+\left (3 x^3+6 x^2 y(x)-3 x y(x)^2+20 y(x)^3\right ) y'(x)+6 x y(x)^2-y(x)^3=0\) [[_homogeneous, `class A`], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓ |
| ODE 692 |
\(\left (a y(x)^3+x^3\right ) y'(x)=x^2 y(x)\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 693 |
\(y'(x) \left (a x^2-b x^3+3 c x y(x)^2+2 c y(x)^3\right )+a y(x)^2+2 b x^3+3 b x^2 y(x)-c y(x)^3=0\) [_rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 694 |
\(x y(x)^3 y'(x)=\left (1-x^2\right ) \left (y(x)^2+1\right )\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 695 |
\(x \left (x-y(x)^3\right ) y'(x)=y(x) \left (y(x)^3+3 x\right )\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 696 |
\(x \left (2 x^3+y(x)^3\right ) y'(x)=y(x) \left (2 x^3-x^2 y(x)+y(x)^3\right )\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 697 |
\(x \left (2 x^3-y(x)^3\right ) y'(x)=y(x) \left (x^3-2 y(x)^3\right )\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 698 |
\(x \left (x^3+3 x^2 y(x)+y(x)^3\right ) y'(x)=y(x)^2 \left (3 x^2+y(x)^2\right )\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 699 |
\(x \left (x^3-2 y(x)^3\right ) y'(x)=y(x) \left (2 x^3-y(x)^3\right )\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 700 |
\(x \left (x^4-2 y(x)^3\right ) y'(x)+y(x) \left (2 x^4+y(x)^3\right )=0\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 701 |
\(x \left (2 y(x)^3+y(x)+x\right ) y'(x)=(x-y(x)) y(x)\) [_rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 702 |
\(\left (-7 x y(x)^3-y(x)+5 x\right ) y'(x)-y(x)^4+5 y(x)=0\) [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 703 |
\(y(x) \left (1-2 x^3 y(x)\right )+x \left (1-2 x y(x)^3\right ) y'(x)=0\) [_rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 704 |
\(x \left (-2 x y(x)^3-x y(x)^2+2\right ) y'(x)+2 y(x)+1=0\) [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]] Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 705 |
\(\left (-10 x^2 y(x)^3+3 y(x)^2+2\right ) y'(x)=x \left (5 y(x)^4+1\right )\) [_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]] Solution method Exact equation Maple ✓ |
| ODE 706 |
\(x y'(x) \left (a+b x y(x)^3\right )+y(x) \left (a+c x^3 y(x)\right )=0\) [_rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 707 |
\(y(x) \left (1-2 x^3 y(x)^2\right )+x \left (1-2 x^2 y(x)^3\right ) y'(x)=0\) [_rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 708 |
\(x (1-x y(x)) \left (1-x^2 y(x)^2\right ) y'(x)+y(x) (x y(x)+1) \left (x^2 y(x)^2+1\right )=0\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 709 |
\(\left (x^2-y(x)^4\right ) y'(x)=x y(x)\) [[_homogeneous, `class G`], _rational] Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 710 |
\(\left (x^3-y(x)^4\right ) y'(x)=3 x^2 y(x)\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 711 |
\(\left (a^2 x^2+\left (x^2+y(x)^2\right )^2\right ) y'(x)=a^2 x y(x)\) [_rational] Solution method Change of Variable, Two new variables Maple ✓ |
| ODE 712 |
\(2 \left (x-y(x)^4\right ) y'(x)=y(x)\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 713 |
\(\left (-2 y(x)^4-x y(x)^3+4 x\right ) y'(x)=y(x) \left (y(x)^3+2\right )\) [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 714 |
\(y(x) y'(x) \left ((a x+b y(x))^3+a x^3\right )+x \left ((a x+b y(x))^3+b y(x)^3\right )=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 715 |
\(\left (2 x^2 y(x)^3+x y(x)^4+2 y(x)+x\right ) y'(x)+y(x) \left (y(x)^4+1\right )=0\) [_rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 716 |
\(2 x \left (x^3+y(x)^4\right ) y'(x)=y(x) \left (x^3+2 y(x)^4\right )\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 717 |
\(x \left (1-x^2 y(x)^4\right ) y'(x)+y(x)=0\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 718 |
\(\left (x^2-y(x)^5\right ) y'(x)=2 x y(x)\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 719 |
\(x \left (x^3+y(x)^5\right ) y'(x)=y(x) \left (x^3-y(x)^5\right )\) [[_homogeneous, `class G`], _rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 720 |
\(y(x)^3 \left (3 x^5 y(x)^5-1\right )+x^3 \left (5 x^3 y(x)^7+1\right ) y'(x)=0\) [_rational] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 721 |
\(y'(x) (\text {f1}(x,y(x))+x \text {f2}(x,y(x)))=y(x) \text {f2}(x,y(x))+\text {f3}(x,y(x))\) [NONE] Solution method Homogeneous equation, Darbooux type Maple ✗ |
| ODE 722 |
\(y'(x) (a (y(x)+x)+1)^n+a (y(x)+x)^n=0\) [[_homogeneous, `class C`], _dAlembert] Solution method Exact equation Maple ✓ |
| ODE 723 |
\(x y'(x) \left (a+x y(x)^n\right )+b y(x)=0\) [[_homogeneous, `class G`], _rational] Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 724 |
\(f(x) y(x)^m y'(x)+g(x) y(x)^{m+1}+h(x) y(x)^n=0\) [_Bernoulli] Solution method The Bernoulli ODE Maple ✓ |
| ODE 725 |
\(\sqrt {b^2+y(x)^2} y'(x)=\sqrt {a^2+x^2}\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 726 |
\(\sqrt {b^2-y(x)^2} y'(x)=\sqrt {a^2-x^2}\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 727 |
\(\sqrt {Y} y'(x)=\sqrt {X}\) [_quadrature] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 728 |
\(\left (\sqrt {y(x)+x}+1\right ) y'(x)+1=0\) [[_homogeneous, `class C`], _dAlembert] Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 729 |
\(\sqrt {x y(x)} y'(x)-y(x)+x=\sqrt {x y(x)}\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 730 |
\(\left (x-2 \sqrt {x y(x)}\right ) y'(x)=y(x)\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 731 |
\(\left (x^2+1\right )^{3/2} \left (y(x)+\sqrt {y(x)^2+1}\right ) y'(x)=y(x)^2+1\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 732 |
\(\left (x^2+1\right )^{3/2} \left (y(x)+\sqrt {y(x)^2+1}\right ) y'(x)=y(x)^2+1\) [_separable] Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 733 |
\(\left (x-\sqrt {x^2+y(x)^2}\right ) y'(x)=y(x)\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 734 |
\(x \left (1-\sqrt {x^2-y(x)^2}\right ) y'(x)=y(x)\) [`y=_G(x,y')`] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 735 |
\(x \left (\sqrt {x^2+y(x)^2}+x\right ) y'(x)+\sqrt {x^2+y(x)^2} y(x)=0\) [[_homogeneous, `class G`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 736 |
\(x y(x) \left (\sqrt {x^2-y(x)^2}+x\right ) y'(x)=x y(x)^2-\left (x^2-y(x)^2\right )^{3/2}\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 737 |
\(\left (x-y(x)^2 \sqrt {y(x)^2-x^2}\right ) y'(x)=y(x) \left (x \sqrt {y(x)^2-x^2}+1\right )\) [NONE] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 738 |
\(\left (x \sqrt {x^2+y(x)^2+1}-y(x) \left (x^2+y(x)^2\right )\right ) y'(x)=\sqrt {x^2+y(x)^2+1} y(x)+x \left (x^2+y(x)^2\right )\) [[_1st_order, _with_linear_symmetries]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 739 |
\(y'(x) \left (x^2 \sec (x) \cos (y(x))+1\right )-y(x) \tan (x)+\sec (x) \sin (y(x))=0\) [NONE] Solution method Exact equation, integrating factor Maple ✗ |
| ODE 740 |
\(y'(x) \cos (y(x)) (\cos (y(x))-\sin (A) \sin (x))+\cos (x) (\cos (x)-\sin (A) \sin (y(x)))=0\) [NONE] Solution method Exact equation Maple ✓ |
| ODE 741 |
\(y'(x) (a \cos (a y(x)+b x)-b \sin (a x+b y(x)))-a \sin (a x+b y(x))+b \cos (a y(x)+b x)=0\) [_exact] Solution method Exact equation Maple ✓ |
| ODE 742 |
\(y'(x) (a \sin (x y(x))-\sin (y(x))+\cos (y(x)+x))+y(x) \sin (x y(x))+\cos (y(x)+x)+\cos (x)=0\) [NONE] Solution method Exact equation Maple ✗ |
| ODE 743 |
\(y'(x) (\cos (x) \sec (y(x))+x)+\tan (y(x))-y(x) \sin (x) \sec (y(x))=0\) [NONE] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 744 |
\(y'(x) \left (x^2+2 y(x) \sin (x) \sec (y(x))\right )+2 x \tan (y(x))+y(x)^2 \cos (x) \sec (y(x))=0\) [NONE] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 745 |
\(y'(x) \left (x^2 \sec ^2(y(x))-6 x y(x)+2\right )-3 y(x)^2+2 x \tan (y(x))=0\) [_exact] Solution method Exact equation Maple ✓ |
| ODE 746 |
\(y'(x) ((y(x)+x) \tan (y(x))+1)+1=0\) [[_1st_order, _with_linear_symmetries]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 747 |
\(x y'(x) \left (x-y(x) \tan \left (\frac {y(x)}{x}\right )\right )+y(x) \left (y(x) \tan \left (\frac {y(x)}{x}\right )+x\right )=0\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous equation Maple ✓ |
| ODE 748 |
\(\left (x e^{y(x)}+e^x\right ) y'(x)+e^x y(x)+e^{y(x)}=0\) [_exact] Solution method Exact equation Maple ✓ |
| ODE 749 |
\(y'(x) (-\log (y(x))-2 x+1)+2 y(x)=0\) [[_1st_order, _with_linear_symmetries]] Solution method Exact equation, integrating factor Maple ✓ |
| ODE 750 |
\(y'(x) (x \cosh (y(x))+\sinh (x))+\sinh (y(x))+y(x) \cosh (x)=0\) [_exact] Solution method Exact equation Maple ✓ |
| ODE 751 |
\((\sinh (x)+1) y'(x) \sinh (y(x))+\cosh (x) (\cosh (y(x))-1)=0\) [_separable] Solution method Exact equation Maple ✓ |
| ODE 752 |
\(y'(x)^2=a x^n\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 753 |
\(y'(x)^2=y(x)\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 754 |
\(y'(x)^2=x-y(x)\) [[_homogeneous, `class C`], _dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 755 |
\(y'(x)^2=x^2+y(x)\) [[_homogeneous, `class G`]] Solution method Homogeneous ODE, The Isobaric equation Maple ✓ |
| ODE 756 |
\(x^2+y'(x)^2=4 y(x)\) [[_homogeneous, `class G`]] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 757 |
\(3 x^2+y'(x)^2=8 y(x)\) [[_homogeneous, `class G`]] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 758 |
\(a x^2+b y(x)+y'(x)^2=0\) [[_homogeneous, `class G`]] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✗ |
| ODE 759 |
\(y'(x)^2=y(x)^2+1\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 760 |
\(y'(x)^2=1-y(x)^2\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 761 |
\(y'(x)^2=a^2-y(x)^2\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 762 |
\(y'(x)^2=a^2 y(x)^2\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 763 |
\(y'(x)^2=a+b y(x)^2\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 764 |
\(y'(x)^2=x^2 y(x)^2\) [_separable] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 765 |
\(y'(x)^2=(y(x)-1) y(x)^2\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 766 |
\(y'(x)^2=(y(x)-a) (y(x)-b) (y(x)-c)\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 767 |
\(y'(x)^2=a^2 y(x)^n\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 768 |
\(y'(x)^2=a^2 y(x)^2 \left (1-\log ^2(y(x))\right )\) [_quadrature] Solution method Change of variable Maple ✓ |
| ODE 769 |
\(f(x) (y(x)-a) (y(x)-b)+y'(x)^2=0\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 770 |
\(f(x) (y(x)-a)^2 (y(x)-b)+y'(x)^2=0\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 771 |
\(f(x) (y(x)-a) (y(x)-b) (y(x)-c)+y'(x)^2=0\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 772 |
\(f(x) (y(x)-a)^2 (y(x)-b) (y(x)-c)+y'(x)^2=0\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 773 |
\(f(x) (y(x)-\text {a1}) (y(x)-\text {a2}) (y(x)-\text {a3}) (y(x)-\text {a4})+y'(x)^2=0\) odeadvisor timed out Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 774 |
\(y'(x)^2=f(x)^2 (y(x)-a) (y(x)-b) (y(x)-c)^2\) [_separable] Solution method Change of variable Maple ✓ |
| ODE 775 |
\(y'(x)^2=f(x)^2 (y(x)-a) (y(x)-b) (y(x)-u(x))^2\) [`y=_G(x,y')`] Solution method Change of variable Maple ✗ |
| ODE 776 |
\(y'(x)^2+2 y'(x)+x=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 777 |
\(a (x-y(x))+y'(x)^2-2 y'(x)=0\) [[_homogeneous, `class C`], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 778 |
\(y'(x)^2-2 y'(x)-y(x)^2=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 779 |
\(y'(x)^2-5 y'(x)+6=0\) [_quadrature] Solution method Missing Variables ODE, Both independent and dependent
variable missing Maple ✓ |
| ODE 780 |
\(y'(x)^2-7 y'(x)+12=0\) [_quadrature] Solution method Missing Variables ODE, Both independent and dependent
variable missing Maple ✓ |
| ODE 781 |
\(a y'(x)+b+y'(x)^2=0\) [_quadrature] Solution method Missing Variables ODE, Both independent and dependent
variable missing Maple ✓ |
| ODE 782 |
\(a y'(x)+b x+y'(x)^2=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(x\) Maple ✓ |
| ODE 783 |
\(a y'(x)+b y(x)+y'(x)^2=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 784 |
\(y'(x)^2+x y'(x)+1=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(x\) Maple ✓ |
| ODE 785 |
\(y'(x)^2+x y'(x)-y(x)=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 786 |
\(y'(x)^2-x y'(x)+y(x)=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 787 |
\(y'(x)^2-x y'(x)-y(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 788 |
\(y'(x)^2+x y'(x)-y(x)+x=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 789 |
\(y'(x)^2+(1-x) y'(x)+y(x)=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 790 |
\(y'(x)^2-(x+1) y'(x)+y(x)=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 791 |
\(y'(x)^2-(2-x) y'(x)-y(x)+1=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 792 |
\((a+x) y'(x)+y'(x)^2-y(x)=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 793 |
\(y'(x)^2-2 x y'(x)+1=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(x\) Maple ✓ |
| ODE 794 |
\(-3 x^2+2 x y'(x)+y'(x)^2=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 795 |
\(y'(x)^2+2 x y'(x)-y(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 796 |
\(y'(x)^2+2 x y'(x)-y(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method Change of variable Maple ✓ |
| ODE 797 |
\(y'(x)^2-2 x y'(x)+2 y(x)=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 798 |
\(y'(x)^2-(2 x+1) y'(x)-(1-x) x=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 799 |
\(y'(x)^2+2 (1-x) y'(x)-2 (x-y(x))=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 800 |
\(y'(x)^2+3 x y'(x)-y(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 801 |
\(y'(x)^2-4 (x+1) y'(x)+4 y(x)=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 802 |
\(a x y'(x)+y'(x)^2=b c x^2\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 803 |
\(-a x y'(x)+a y(x)+y'(x)^2=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 804 |
\(a x y'(x)+b x^2+c y(x)+y'(x)^2=0\) [[_homogeneous, `class G`]] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✗ |
| ODE 805 |
\((a+b x) y'(x)+c+y'(x)^2=b y(x)\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 806 |
\(-2 x^2 y'(x)+2 x y'(x)+y'(x)^2=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 807 |
\(a x^2 y'(x)+b x y(x)+y'(x)^2=0\) [[_homogeneous, `class G`]] Solution method Homogeneous ODE, The Isobaric equation Maple ✓ |
| ODE 808 |
\(a x^3 y'(x)-2 a x^2 y(x)+y'(x)^2=0\) [[_1st_order, _with_linear_symmetries]] Solution method Homogeneous ODE, The Isobaric equation Maple ✓ |
| ODE 809 |
\(-2 a x^3 y'(x)+4 a x^2 y(x)+y'(x)^2=0\) [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓ |
| ODE 810 |
\(4 x^5 y'(x)-12 x^4 y(x)+y'(x)^2=0\) [[_1st_order, _with_linear_symmetries]] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 811 |
\(y'(x)^2-2 \cosh (x) y'(x)+1=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 812 |
\(y'(x)^2+y(x) y'(x)=x (y(x)+x)\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 813 |
\(y'(x)^2-y(x) y'(x)+e^x=0\) [[_1st_order, _with_linear_symmetries]] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 814 |
\(y'(x)^2+(y(x)+x) y'(x)+x y(x)=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 815 |
\(y'(x)^2-2 y(x) y'(x)-2 x=0\) [_dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 816 |
\(y'(x)^2+(2 y(x)+1) y'(x)+(y(x)-1) y(x)=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Use new
variable Maple ✓ |
| ODE 817 |
\(y'(x)^2-2 (x-y(x)) y'(x)-4 x y(x)=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 818 |
\(y'(x)^2-(4 y(x)+1) y'(x)+y(x) (4 y(x)+1)=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 819 |
\(y'(x)^2-2 (1-3 y(x)) y'(x)-(4-9 y(x)) y(x)=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 820 |
\(y(x) (3 a+b+9 y(x))+(a+6 y(x)) y'(x)+y'(x)^2=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 821 |
\(a y(x) y'(x)-a x+y'(x)^2=0\) [_dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 822 |
\(-a y(x) y'(x)-a x+y'(x)^2=0\) [_dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 823 |
\(y'(x) (a x+b y(x))+a b x y(x)+y'(x)^2=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 824 |
\(y(x)^2 \log (a y(x))-x y(x) y'(x)+y'(x)^2=0\) [[_1st_order, `_with_symmetry_[F(x),G(y)]`]] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 825 |
\(y'(x)^2-(2 x y(x)+1) y'(x)+2 x y(x)=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 826 |
\(y'(x)^2-\left (y(x)^2+4\right ) y'(x)+y(x)^2+4=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Use new
variable Maple ✓ |
| ODE 827 |
\(-(x-y(x)) y(x) y'(x)+y'(x)^2-x y(x)^3=0\) [_separable] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 828 |
\(x y(x)^2 y'(x)+y'(x)^2+y(x)^3=0\) [[_homogeneous, `class G`]] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 829 |
\(-2 x^3 y(x)^2 y'(x)-4 x^2 y(x)^3+y'(x)^2=0\) [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓ |
| ODE 830 |
\(x^4 y(x)^4-x \left (x^2+y(x)^2\right ) y(x) y'(x)+y'(x)^2=0\) [_separable] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 831 |
\(2 x y(x)^3 y'(x)+y'(x)^2+y(x)^4=0\) [[_homogeneous, `class G`]] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 832 |
\(y'(x)^2+2 y(x) \cot (x) y'(x)-y(x)^2=0\) [_separable] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 833 |
\(y'(x)^2-3 x y(x)^{2/3} y'(x)+9 y(x)^{5/3}=0\) [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓ |
| ODE 834 |
\(y'(x)^2=e^{4 x-2 y(x)} \left (y'(x)-1\right )\) [[_homogeneous, `class C`], _dAlembert] Solution method Change of variable Maple ✓ |
| ODE 835 |
\(2 y'(x)^2+x y'(x)-2 y(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 836 |
\(2 y'(x)^2-(1-x) y'(x)-y(x)=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 837 |
\(-2 x^2 y'(x)+2 y'(x)^2+3 x y(x)=0\) [[_homogeneous, `class G`]] Solution method Homogeneous ODE, The Isobaric equation Maple ✓ |
| ODE 838 |
\(2 y'(x)^2+2 (6 y(x)-1) y'(x)+3 y(x) (6 y(x)-1)=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 839 |
\(3 y'(x)^2-2 x y'(x)+y(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 840 |
\(x^2+4 x y'(x)+3 y'(x)^2-y(x)=0\) [[_homogeneous, `class G`]] Solution method Change of variable Maple ✓ |
| ODE 841 |
\(4 y'(x)^2=9 x\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 842 |
\(4 y'(x)^2+2 x e^{-2 y(x)} y'(x)-e^{-2 y(x)}=0\) [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓ |
| ODE 843 |
\(4 y'(x)^2+2 e^{2 x-2 y(x)} y'(x)-e^{2 x-2 y(x)}=0\) [[_homogeneous, `class C`], _dAlembert] Solution method Change of variable Maple ✓ |
| ODE 844 |
\(5 y'(x)^2+3 x y'(x)-y(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 845 |
\(5 y'(x)^2+6 x y'(x)-2 y(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 846 |
\(3 x y(x)^4 y'(x)+9 y'(x)^2+y(x)^5=0\) [[_1st_order, _with_linear_symmetries]] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 847 |
\(x y'(x)^2=a\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 848 |
\(x y'(x)^2=a-x^2\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 849 |
\(x y'(x)^2=y(x)\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 850 |
\(x y'(x)^2-2 y(x)+x=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 851 |
\(x y'(x)^2+y'(x)=y(x)\) [_rational, _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 852 |
\(x y'(x)^2+2 y'(x)-y(x)=0\) [_rational, _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 853 |
\(x y'(x)^2-2 y'(x)-y(x)=0\) [_rational, _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 854 |
\(x y'(x)^2+4 y'(x)-2 y(x)=0\) [_rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 855 |
\(x y'(x)^2+x y'(x)-y(x)=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 856 |
\(-\left (x^2+1\right ) y'(x)+x y'(x)^2+x=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 857 |
\(a+x y'(x)^2+y(x) y'(x)=0\) [[_homogeneous, `class G`], _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 858 |
\(a+x y'(x)^2-y(x) y'(x)=0\) [[_homogeneous, `class G`], _rational, _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 859 |
\(a x+x y'(x)^2-y(x) y'(x)=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 860 |
\(-x^2+x y'(x)^2+y(x) y'(x)=0\) [[_homogeneous, `class G`]] Solution method Homogeneous ODE, The Isobaric equation Maple ✓ |
| ODE 861 |
\(x^3+x y'(x)^2+y(x) y'(x)=0\) [[_homogeneous, `class G`]] Solution method Homogeneous ODE, The Isobaric equation Maple ✓ |
| ODE 862 |
\(a y(x)+x y'(x)^2-y(x) y'(x)=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 863 |
\(y(x) y'(x)+x y'(x)^2-y(x)^4=0\) [[_homogeneous, `class G`]] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 864 |
\((a-y(x)) y'(x)+b+x y'(x)^2=0\) [[_1st_order, _with_linear_symmetries], _rational, _Clairaut] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 865 |
\(x y'(x)^2+(x-y(x)) y'(x)-y(x)+1=0\) [[_1st_order, _with_linear_symmetries], _rational, _dAlembert] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 866 |
\((a-y(x)+x) y'(x)+x y'(x)^2-y(x)=0\) [[_1st_order, _with_linear_symmetries], _rational, _dAlembert] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 867 |
\(x y'(x)^2-(3 x-y(x)) y'(x)+y(x)=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 868 |
\(a-b y(x)+b x+x y'(x)^2-y(x)=0\) [[_homogeneous, `class C`], _rational, _dAlembert] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 869 |
\(a+x y'(x)^2-2 y(x) y'(x)=0\) [[_homogeneous, `class G`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 870 |
\(x y'(x)^2+2 y(x) y'(x)-x=0\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\) Maple ✓ |
| ODE 871 |
\(a x+x y'(x)^2-2 y(x) y'(x)=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(y\) Maple ✓ |
| ODE 872 |
\(x y'(x)^2-2 y(x) y'(x)+2 y(x)+x=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Change of variable Maple ✓ |
| ODE 873 |
\(9 x^2+x y'(x)^2-3 y(x) y'(x)=0\) [[_homogeneous, `class G`]] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 874 |
\(x y'(x)^2-(3 y(x)+2 x) y'(x)+6 y(x)=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 875 |
\(-a y(x) y'(x)+b+x y'(x)^2=0\) [[_homogeneous, `class G`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 876 |
\(a y(x) y'(x)+b x+x y'(x)^2=0\) [[_homogeneous, `class A`], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 877 |
\(x y'(x)^2-(x y(x)+1) y'(x)+y(x)=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 878 |
\((1-x) y(x) y'(x)+x y'(x)^2-y(x)^2=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 879 |
\(\left (1-x^2 y(x)\right ) y'(x)+x y'(x)^2-x y(x)=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 880 |
\((x+1) y'(x)^2=y(x)\) [[_homogeneous, `class C`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 881 |
\((x+1) y'(x)^2-(y(x)+x) y'(x)+y(x)=0\) [[_1st_order, _with_linear_symmetries], _rational, _dAlembert] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 882 |
\((a-x) y'(x)^2-b+y(x) y'(x)=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 883 |
\((a+x) y'(x)^2+y'(x) (\text {a1}+\text {b1} x+\text {c1} y(x))+\text {a2}+\text {b2} x+\text {c2} y(x)=0\) [_rational, _dAlembert] Solution method Change of variable Maple ✓ |
| ODE 884 |
\(2 x y'(x)^2+(2 x-y(x)) y'(x)-y(x)+1=0\) [_rational, _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 885 |
\(3 x y'(x)^2-6 y(x) y'(x)+2 y(x)+x=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 886 |
\((3 x+1) y'(x)^2-3 (y(x)+2) y'(x)+9=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 887 |
\((3 x+5) y'(x)^2-(3 y(x)+3) y'(x)+y(x)=0\) [_rational, _dAlembert] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 888 |
\(4 x y'(x)^2=(a-3 x)^2\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 889 |
\(4 x y'(x)^2+2 x y'(x)-y(x)=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 890 |
\(4 x y'(x)^2-3 y(x) y'(x)+3=0\) [[_homogeneous, `class G`], _rational, _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 891 |
\(4 x y'(x)^2+4 y(x) y'(x)=1\) [[_homogeneous, `class G`], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 892 |
\(4 y(x) y'(x)+4 x y'(x)^2-y(x)^4=0\) [[_homogeneous, `class G`]] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 893 |
\(4 (2-x) y'(x)^2+1=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 894 |
\(8 y(x) y'(x)+16 x y'(x)^2+y(x)^6=0\) [[_homogeneous, `class G`]] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 895 |
\(x^2 y'(x)^2=a^2\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 896 |
\(x^2 y'(x)^2=y(x)^2\) [_separable] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 897 |
\(x^2 y'(x)^2+x^2-y(x)^2=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 898 |
\(x^2 y'(x)^2=(x-y(x))^2\) [_linear] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 899 |
\(x^2 y'(x)^2-y(x)^4+y(x)^2=0\) [_separable] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 900 |
\(x^2 y'(x)^2-x y'(x)+(1-y(x)) y(x)=0\) [_separable] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 901 |
\(a^2+2 a x y'(x)-2 a y(x)+x^2 y'(x)^2+x^2=0\) [_rational] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 902 |
\(x^2 y'(x)^2-2 x y(x) y'(x)+y(x) (y(x)+1)-x=0\) [[_1st_order, _with_linear_symmetries], _rational] Solution method Change of variable Maple ✓ |
| ODE 903 |
\(-x^4+x^2 y'(x)^2+\left (1-x^2\right ) y(x)^2-2 x y(x) y'(x)=0\) [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Change of variable Maple ✓ |
| ODE 904 |
\(x^2 y'(x)^2-(2 x y(x)+1) y'(x)+y(x)^2+1=0\) [[_1st_order, _with_linear_symmetries], _rational, _Clairaut] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 905 |
\(-(a+2 x y(x)) y'(x)+x^2 y'(x)^2+y(x)^2=0\) [[_homogeneous, `class G`], _rational, _Clairaut] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 906 |
\(x^2 y'(x)^2-x (x-2 y(x)) y'(x)+y(x)^2=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Change of variable Maple ✓ |
| ODE 907 |
\(-4 a+x^2 y'(x)^2+2 x (y(x)+2 x) y'(x)+y(x)^2=0\) [[_1st_order, `_with_symmetry_[F(x),G(y)]`]] Solution method Change of variable Maple ✓ |
| ODE 908 |
\(x \left (x^3-2 y(x)\right ) y'(x)-\left (2 x^3-y(x)\right ) y(x)+x^2 y'(x)^2=0\) [[_homogeneous, `class G`], _rational] Solution method Change of variable Maple ✓ |
| ODE 909 |
\(x^2 y'(x)^2+3 x y(x) y'(x)+2 y(x)^2=0\) [_separable] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\) Maple ✓ |
| ODE 910 |
\(x^3+x^2 y'(x)^2-3 x y(x) y'(x)+2 y(x)^2=0\) [[_homogeneous, `class G`], _rational] Solution method Change of variable Maple ✓ |
| ODE 911 |
\(x^2 y'(x)^2+4 x y(x) y'(x)-5 y(x)^2=0\) [_separable] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 912 |
\(x^2 y'(x)^2-4 x (y(x)+2) y'(x)+4 y(x) (y(x)+2)=0\) [_separable] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 913 |
\(x^2 y'(x)^2-5 x y(x) y'(x)+6 y(x)^2=0\) [_separable] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 914 |
\(x^2 y'(x)^2+x \left (x^2+x y(x)-2 y(x)\right ) y'(x)+(1-x) \left (x^2-y(x)\right ) y(x)=0\) [_rational] Solution method Change of variable Maple ✗ |
| ODE 915 |
\(x^2 y'(x)^2+(y(x)+2 x) y(x) y'(x)+y(x)^2=0\) [[_homogeneous, `class A`], _dAlembert] Solution method Change of variable Maple ✓ |
| ODE 916 |
\(x^2 y'(x)^2+(2 x-y(x)) y(x) y'(x)+y(x)^2=0\) [[_homogeneous, `class A`], _dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 917 |
\(y'(x) \left (a+b x^2 y(x)^3\right )+a b y(x)^3+x^2 y'(x)^2=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 918 |
\(\left (1-x^2\right ) y'(x)^2=1-y(x)^2\) [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✗ |
| ODE 919 |
\(\left (1-x^2\right ) y'(x)^2+4 x^2+2 x y(x) y'(x)=0\) [[_1st_order, `_with_symmetry_[F(x),G(y)]`]] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 920 |
\(\left (a^2+x^2\right ) y'(x)^2=b^2\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 921 |
\(\left (a^2-x^2\right ) y'(x)^2+b^2=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 922 |
\(\left (a^2-x^2\right ) y'(x)^2=b^2\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 923 |
\(\left (a^2-x^2\right ) y'(x)^2=x^2\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 924 |
\(\left (a^2-x^2\right ) y'(x)^2+x^2+2 x y(x) y'(x)=0\) [[_1st_order, `_with_symmetry_[F(x),G(y)]`]] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 925 |
\(\left (a^2-x^2\right ) y'(x)^2-2 x y(x) y'(x)-y(x)^2=0\) [_separable] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 926 |
\(\left (a^2+x^2\right ) y'(x)^2+b-2 x y(x) y'(x)+y(x)^2=0\) [[_1st_order, _with_linear_symmetries], _rational, _Clairaut] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 927 |
\(\left (2 x^2+1\right ) y'(x)^2+\left (x^2+2 x y(x)+y(x)^2+2\right ) y'(x)+2 y(x)^2+1=0\) [`y=_G(x,y')`] Solution method Change of variable Maple ✗ |
| ODE 928 |
\(4 x^2 y'(x)^2-4 x y(x) y'(x)=8 x^3-y(x)^2\) [_linear] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 929 |
\(a x^2 y'(x)^2+(1-a) a x^2-2 a x y(x) y'(x)+y(x)^2=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\) Maple ✓ |
| ODE 930 |
\(\left (1-a^2\right ) x^2 y'(x)^2-a^2 x^2-2 x y(x) y'(x)+y(x)^2=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 931 |
\(x^3 y'(x)^2=a\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 932 |
\(x^3 y'(x)^2+x y'(x)-y(x)=0\) [[_homogeneous, `class G`], _rational] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✗ |
| ODE 933 |
\(a+x^3 y'(x)^2+x^2 y(x) y'(x)=0\) [[_homogeneous, `class G`], _rational] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 934 |
\(x^3 y'(x)^2-\left (2 x^2 y(x)+1\right ) y'(x)+x y(x)^2=0\) [[_homogeneous, `class G`], _rational] Solution method Change of variable Maple ✓ |
| ODE 935 |
\(x \left (1-x^2\right ) y'(x)^2-2 \left (1-x^2\right ) y(x) y'(x)+x \left (1-y(x)^2\right )=0\) [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Change of variable Maple ✓ |
| ODE 936 |
\(4 x (a-x) (b-x) y'(x)^2=\left (-2 x (a+b)+a b+2 x^2\right )^2\) [_quadrature] Solution method Change of variable Maple ✓ |
| ODE 937 |
\(x^4 y'(x)^2-x y'(x)-y(x)=0\) [[_homogeneous, `class G`], _rational] Solution method Homogeneous ODE, The Isobaric equation Maple ✓ |
| ODE 938 |
\(x^4 y'(x)^2+2 x^3 y(x) y'(x)-4=0\) [[_homogeneous, `class G`], _rational] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 939 |
\(x^4 y'(x)^2+x y(x)^2 y'(x)-y(x)^3=0\) [[_homogeneous, `class G`]] Solution method Change of variable Maple ✓ |
| ODE 940 |
\(x^2 \left (a^2-x^2\right ) y'(x)^2+1=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 941 |
\(3 x^4 y'(x)^2-x y(x)-y(x)=0\) [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 942 |
\(4 x^5 y'(x)^2+12 x^4 y(x) y'(x)+9=0\) [[_homogeneous, `class G`]] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 943 |
\(x^6 y'(x)^2-2 x y'(x)-4 y(x)=0\) [[_homogeneous, `class G`], _rational] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 944 |
\(x^8 y'(x)^2+3 x y'(x)+9 y(x)=0\) [[_homogeneous, `class G`]] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 945 |
\(y(x) y'(x)^2=a\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 946 |
\(y(x) y'(x)^2=a^2 x\) [[_homogeneous, `class A`], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 947 |
\(y(x) y'(x)^2=e^{2 x}\) [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓ |
| ODE 948 |
\(2 a x y'(x)-a y(x)+y(x) y'(x)^2=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\) Maple ✓ |
| ODE 949 |
\(-4 a^2 x y'(x)+a^2 y(x)+y(x) y'(x)^2=0\) [[_homogeneous, `class A`], _dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 950 |
\(a x y'(x)+b y(x)+y(x) y'(x)^2=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 951 |
\(-(a-2 b x) y'(x)-b y(x)+y(x) y'(x)^2=0\) [[_homogeneous, `class C`], _rational, _dAlembert] Solution method Change of variable Maple ✓ |
| ODE 952 |
\(x^3 y'(x)-x^2 y(x)+y(x) y'(x)^2=0\) [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓ |
| ODE 953 |
\(y(x) y'(x)^2+(x-y(x)) y'(x)-x=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 954 |
\(y(x) y'(x)^2-(y(x)+x) y'(x)+y(x)=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 955 |
\(y(x) y'(x)^2-(x y(x)+1) y'(x)+x=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 956 |
\(y(x) y'(x)^2+\left (x-y(x)^2\right ) y'(x)-x y(x)=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 957 |
\(y(x) y'(x)^2+y(x)=a\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Use new
variable Maple ✓ |
| ODE 958 |
\((y(x)+x) y'(x)^2+2 x y'(x)-y(x)=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 959 |
\((2 x-y(x)) y'(x)^2-2 (1-x) y'(x)-y(x)+2=0\) [[_homogeneous, `class C`], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 960 |
\(2 y(x) y'(x)^2+(5-4 x) y'(x)+2 y(x)=0\) [[_homogeneous, `class C`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 961 |
\(4 x^3 y'(x)-4 x^2 y(x)+9 y(x) y'(x)^2=0\) [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓ |
| ODE 962 |
\((1-a y(x)) y'(x)^2=a y(x)\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Use new
variable Maple ✓ |
| ODE 963 |
\(y'(x)^2 (\text {a0}+\text {b0} x+\text {c0} y(x))+y'(x) (\text {a1}+\text {b1} x+\text {c1} y(x))+\text {a2}+\text {b2} x+\text {c2} y(x)=0\) [_rational, _dAlembert] Solution method Change of variable Maple ✓ |
| ODE 964 |
\(\left (x^2-a y(x)\right ) y'(x)^2-2 x y(x) y'(x)=0\) [_quadrature] Solution method Change of variable Maple ✓ |
| ODE 965 |
\(x y(x) y'(x)^2+(y(x)+x) y'(x)+1=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 966 |
\(\left (x^2+y(x)^2\right ) y'(x)+x y(x) y'(x)^2+x y(x)=0\) [_separable] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 967 |
\(\left (x^2-y(x)^2\right ) y'(x)+x y(x) y'(x)^2-x y(x)=0\) [_separable] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 968 |
\(-\left (x^2-y(x)^2\right ) y'(x)+x y(x) y'(x)^2-x y(x)=0\) [_separable] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 969 |
\(\left (a+x^2-y(x)^2\right ) y'(x)+x y(x) y'(x)^2-x y(x)=0\) [_rational] Solution method Change of variable Maple ✗ |
| ODE 970 |
\(-y'(x) \left (a-b x^2+y(x)^2\right )-b x y(x)+x y(x) y'(x)^2=0\) [_rational] Solution method The method of Lagrange Maple ✗ |
| ODE 971 |
\(\left (3 x^2-2 y(x)^2\right ) y'(x)+x y(x) y'(x)^2-6 x y(x)=0\) [_separable] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 972 |
\(-2 x y(x) y'(x)+x (x-2 y(x)) y'(x)^2+y(x)^2-2 x y(x)=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\) Maple ✓ |
| ODE 973 |
\(6 x y(x) y'(x)+x (x-2 y(x)) y'(x)^2+y(x)^2-2 x y(x)=0\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\) Maple ✓ |
| ODE 974 |
\(y(x)^2 y'(x)^2=a^2\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 975 |
\(-a^2+y(x)^2 y'(x)^2+y(x)^2=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 976 |
\(y(x)^2 y'(x)^2-3 x y'(x)+y(x)=0\) [[_1st_order, _with_linear_symmetries], _rational] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 977 |
\(-6 x^3 y'(x)+4 x^2 y(x)+y(x)^2 y'(x)^2=0\) [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓ |
| ODE 978 |
\(4 a^2-4 a y(x) y'(x)-4 a x+y(x)^2 y'(x)^2+y(x)^2=0\) [_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]] Solution method Change of variable Maple ✓ |
| ODE 979 |
\(y(x)^2 y'(x)^2-(x+1) y(x) y'(x)+x=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 980 |
\(x^2+2 x y(x) y'(x)+y(x)^2 y'(x)^2=0\) [_separable] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\) Maple ✓ |
| ODE 981 |
\(a+y(x)^2 y'(x)^2+2 x y(x) y'(x)-y(x)^2=0\) [_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]] Solution method Change of variable Maple ✗ |
| ODE 982 |
\(-x^2-2 x y(x) y'(x)+y(x)^2 y'(x)^2+2 y(x)^2=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Change of variable Maple ✓ |
| ODE 983 |
\(a-x^2-2 x y(x) y'(x)+y(x)^2 y'(x)^2+2 y(x)^2=0\) [_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]] Solution method Change of variable Maple ✓ |
| ODE 984 |
\((a-1) b+a x^2+2 a x y(x) y'(x)+(1-a) y(x)^2+y(x)^2 y'(x)^2=0\) [_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(x\) Maple ✓ |
| ODE 985 |
\(\left (1-y(x)^2\right ) y'(x)^2=1\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 986 |
\(\left (a^2-y(x)^2\right ) y'(x)^2=y(x)^2\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 987 |
\(\left (a^2-2 a x y(x)+y(x)^2\right ) y'(x)^2+2 a y(x) y'(x)+y(x)^2=0\) [`y=_G(x,y')`] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✗ |
| ODE 988 |
\(\left (a^2 x^2-y(x)^2\right ) y'(x)^2+\left (a^2-1\right ) x^2-2 x y(x) y'(x)=0\) [[_homogeneous, `class A`], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 989 |
\(\left ((1-a) x^2+y(x)^2\right ) y'(x)^2+2 a x y(x) y'(x)+(1-a) y(x)^2+x^2=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\) Maple ✓ |
| ODE 990 |
\(\left (\left (1-4 a^2\right ) x^2+y(x)^2\right ) y'(x)^2-8 a^2 x y(x) y'(x)+\left (1-4 a^2\right ) y(x)^2+x^2=0\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\) Maple ✓ |
| ODE 991 |
\(\left (\left (1-a^2\right ) x^2+y(x)^2\right ) y'(x)^2+2 a^2 x y(x) y'(x)+\left (1-a^2\right ) y(x)^2+x^2=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\) Maple ✓ |
| ODE 992 |
\((y(x)+x)^2 y'(x)^2=y(x)^2\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 993 |
\(-\left (x^2-x y(x)-2 y(x)^2\right ) y'(x)+(y(x)+x)^2 y'(x)^2-(x-y(x)) y(x)=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 994 |
\(2 a^2 y'(x)+\left (a^2-(x-y(x))^2\right ) y'(x)^2+a^2-(x-y(x))^2=0\) [[_homogeneous, `class C`], _dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 995 |
\(x^2+2 x y(x) y'(x)+2 y(x)^2 y'(x)^2+y(x)^2-1=0\) [_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]] Solution method Change of variable Maple ✓ |
| ODE 996 |
\(-x^2-2 x y(x) y'(x)+3 y(x)^2 y'(x)^2+4 y(x)^2=0\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(x\) Maple ✓ |
| ODE 997 |
\(3 x^3+2 (3 x+1) x y(x) y'(x)+4 y(x)^2 y'(x)^2=0\) [_separable] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 998 |
\(\left (x^2-4 y(x)^2\right ) y'(x)^2-4 x^2+6 x y(x) y'(x)+y(x)^2=0\) [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 999 |
\(9 y(x)^2 y'(x)^2-3 x y'(x)+y(x)=0\) [[_1st_order, _with_linear_symmetries], _rational] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1000 |
\((2-3 y(x))^2 y'(x)^2=4 (1-y(x))\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 1001 |
\(a^2 \left (-x^2\right )-3 a^2 x y(x) y'(x)+\left (1-a^2\right ) y(x)^2 y'(x)^2+y(x)^2=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Change of variable Maple ✓ |
| ODE 1002 |
\((a-b) y(x)^2 y'(x)^2-a b+a y(x)^2-b x^2-2 b x y(x) y'(x)=0\) [_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]] Solution method Change of variable Maple ✓ |
| ODE 1003 |
\(a^2 y'(x)^2 \left (b^2-(c x-a y(x))^2\right )+c^2 \left (b^2-(c x-a y(x))^2\right )+2 a b^2 c y'(x)=0\) [[_homogeneous, `class C`], _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 1004 |
\(a^2 x+y(x)^3 \left (-y'(x)\right )+x y(x)^2 y'(x)^2=0\) [[_homogeneous, `class G`], _rational] Solution method Change of variable Maple ✓ |
| ODE 1005 |
\(\left (a-x^3-y(x)^3\right ) y'(x)+x^2 y(x)+x y(x)^2 y'(x)^2=0\) [_rational] Solution method Change of variable Maple ✓ |
| ODE 1006 |
\(-x \left (x^2-2 y(x)^2\right )-2 y(x)^3 y'(x)+x y(x)^2 y'(x)^2=0\) [_separable] Solution method Change of variable Maple ✓ |
| ODE 1007 |
\(-a+y(x)^3 \left (-y'(x)\right )+2 x y(x)^2 y'(x)^2=0\) [[_homogeneous, `class G`], _rational] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1008 |
\(4 x^2 y(x)^2 y'(x)^2=\left (x^2+y(x)^2\right )^2\) [[_homogeneous, `class A`], _rational, _Bernoulli] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 1009 |
\(-2 x \left (x^3+2 y(x)^2\right ) y(x) y'(x)+\left (2 x^3+y(x)^2\right ) y(x)^2+4 x^2 y(x)^2 y'(x)^2=0\) [[_homogeneous, `class G`], _rational] Solution method Change of variable Maple ✓ |
| ODE 1010 |
\(4 y(x)^3 y'(x)^2-4 x y'(x)+y(x)=0\) [[_1st_order, _with_linear_symmetries], _rational] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1011 |
\(x y(x) \left (x^2+y(x)^2\right ) y'(x)^2-x y(x) \left (x^2+y(x)^2\right )-\left (x^4+x^2 y(x)^2+y(x)^4\right ) y'(x)=0\) [[_homogeneous, `class A`], _rational, _Bernoulli] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\) Maple ✓ |
| ODE 1012 |
\(x \left (a^2 x+y(x) \left (x^2-y(x)^2\right )\right ) y'(x)^2+\left (2 a^2 x y(x)+\left (x^2-y(x)^2\right )^2\right ) y'(x)+a^2 y(x)^2-x \left (x^2-y(x)^2\right ) y(x)=0\) [`y=_G(x,y')`] Solution method Change of variable Maple ✗ |
| ODE 1013 |
\(x \left (a^2 x+y(x) \left (x^2-y(x)^2\right )\right ) y'(x)^2-\left (2 a^2 x y(x)-\left (x^2-y(x)^2\right )^2\right ) y'(x)+a^2 y(x)^2-x \left (x^2-y(x)^2\right ) y(x)=0\) [_separable] Solution method Change of variable Maple ✗ |
| ODE 1014 |
\(\left (x^2-y(x)^2 \left (x^2+y(x)^2\right )\right ) y'(x)^2-2 x y(x) y'(x)+y(x)^2=0\) [`y=_G(x,y')`] Solution method Change of variable Maple ✓ |
| ODE 1015 |
\(-2 x \left (x^2+2 y(x)^2\right ) y(x) y'(x)+\left (x^4+y(x)^2 \left (x^2-y(x)^2\right )\right ) y'(x)^2+y(x)^4=0\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\) Maple ✓ |
| ODE 1016 |
\(y(x)^5 \left (-y'(x)\right )+3 x y(x)^4 y'(x)^2+1=0\) [[_homogeneous, `class G`], _rational] Solution method Change of variable Maple ✓ |
| ODE 1017 |
\(-a-3 y(x)^5 y'(x)+9 x y(x)^4 y'(x)^2=0\) [[_homogeneous, `class G`], _rational] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1018 |
\(9 \left (1-x^2\right ) y(x)^4 y'(x)^2+4 x^2+6 x y(x)^5 y'(x)=0\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Change of variable Maple ✓ |
| ODE 1019 |
\(y'(x)^2 \left (a^2 r(x,y(x))-x^2\right )+a^2 r(x,y(x))+2 x y(x) y'(x)-y(x)^2=0\) [NONE] Solution method Change of variable, polar coordinates Maple ✗ |
| ODE 1020 |
\(y'(x)^2 \left (a r(x,y(x))-x^2\right )+a r(x,y(x))+2 x y(x) y'(x)-y(x)^2=0\) [NONE] Solution method Change of variable, polar coordinates Maple ✗ |
| ODE 1021 |
\(y'(x)^3=a+b x\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 1022 |
\(y'(x)^3=a x^n\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 1023 |
\(y'(x)^3-y(x)+x=0\) [[_homogeneous, `class C`], _dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1024 |
\(y'(x)^3=f(x) \left (a+b y(x)+c y(x)^2\right )\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 1025 |
\(y'(x)^3=(y(x)-a)^2 (y(x)-b)^2\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 1026 |
\(f(x) (y(x)-a)^2 (y(x)-b)^2+y'(x)^3=0\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 1027 |
\(f(x) (y(x)-a)^2 (y(x)-b)^2 (y(x)-c)^2+y'(x)^3=0\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 1028 |
\(a-b x+y'(x)^3+y'(x)=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(x\) Maple ✓ |
| ODE 1029 |
\(y'(x)^3+y'(x)-y(x)=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 1030 |
\(y'(x)^3+y'(x)=e^{y(x)}\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 1031 |
\(y'(x)^3-7 y'(x)+6=0\) [_quadrature] Solution method Missing Variables ODE, Both independent and dependent
variable missing Maple ✓ |
| ODE 1032 |
\(a y(x)+y'(x)^3-x y'(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1033 |
\(y'(x)^3+2 x y'(x)-y(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1034 |
\(y'(x)^3-2 x y'(x)-y(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1035 |
\(-a x y'(x)+x^3+y'(x)^3=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Use new
variable Maple ✓ |
| ODE 1036 |
\(a x y'(x)-a y(x)+y'(x)^3=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 1037 |
\(-(a+b x) y'(x)+b y(x)+y'(x)^3=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 1038 |
\(y'(x)^3-y(x) y'(x)-x=0\) [_dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 1039 |
\(y'(x)^3-(y(x)+3) y'(x)+x=0\) [_dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1040 |
\(y'(x)^3-2 y(x) y'(x)+y(x)^2=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 1041 |
\(-a x y(x) y'(x)+2 a y(x)^2+y'(x)^3=0\) [[_1st_order, _with_linear_symmetries]] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1042 |
\(-\left (x^3+x y(x)+y(x)^2\right ) y'(x)+y'(x)^3+x y(x) (y(x)+x)=0\) [`y=_G(x,y')`] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✗ |
| ODE 1043 |
\(-x y(x)^4 y'(x)+y'(x)^3-y(x)^5=0\) [[_1st_order, _with_linear_symmetries]] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1044 |
\(y'(x)^3+e^{3 x-2 y(x)} \left (y'(x)-1\right )=0\) [[_homogeneous, `class C`], _dAlembert] Solution method Change of variable Maple ✗ |
| ODE 1045 |
\(y'(x)^3+\left (e^{2 x}+e^{3 x}\right ) e^{-2 y(x)} y'(x)-e^{3 x-2 y(x)}=0\) [`y=_G(x,y')`] Solution method Change of variable Maple ✓ |
| ODE 1046 |
\(y'(x)^3+y'(x)^2-y(x)=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 1047 |
\(y'(x)^3-y'(x)^2+y(x)^2=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Use new
variable Maple ✓ |
| ODE 1048 |
\(y'(x)^3-y'(x)^2+x y'(x)-y(x)=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 1049 |
\(a b x-a y'(x)^2+b y(x)+y'(x)^3=0\) [[_homogeneous, `class C`], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1050 |
\(\text {a0} y'(x)^2+\text {a1} y'(x)+\text {a2}+\text {a3} y(x)+y'(x)^3=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 1051 |
\(y'(x)^3+x y'(x)^2-y(x)=0\) [_dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1052 |
\(-x^3-(1-3 x) x y'(x)+y'(x)^3+(1-3 x) y'(x)^2-1=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Use new
variable Maple ✓ |
| ODE 1053 |
\(y'(x)^3-y(x) y'(x)^2+y(x)^2=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 1054 |
\(y'(x)^3+y'(x)^2 (\cos (x) \cot (x)-y(x))-y'(x) (y(x) \cos (x) \cot (x)+1)+y(x)=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 1055 |
\(y'(x)^3+\left (2 x-y(x)^2\right ) y'(x)^2-2 x y(x)^2 y'(x)=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 1056 |
\(\left (x^2+2 x y(x)^2-y(x)^2\right ) y'(x)-y(x)^2 \left (x^2-y(x)^2\right )+y'(x)^3-\left (y(x)^2+2 x\right ) y'(x)^2=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 1057 |
\(-x^3 y(x)^3+x \left (x^2+x y(x)+y(x)^2\right ) y(x) y'(x)-\left (x^2+x y(x)+y(x)^2\right ) y'(x)^2+y'(x)^3=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 1058 |
\(-x^3 y(x)^6+x \left (x^2+y(x)^4+x y(x)^2\right ) y(x)^2 y'(x)-\left (x^2+y(x)^4+x y(x)^2\right ) y'(x)^2+y'(x)^3=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 1059 |
\(2 y'(x)^3+x y'(x)-2 y(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 1060 |
\(2 y'(x)^3+y'(x)^2-y(x)=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 1061 |
\(x^4 \left (-y'(x)\right )+2 x^3 y(x)+3 y'(x)^3=0\) [[_1st_order, _with_linear_symmetries]] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1062 |
\(4 y'(x)^3+4 y'(x)=x\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(x\) Maple ✓ |
| ODE 1063 |
\(8 y'(x)^3+12 y'(x)^2=27 (y(x)+x)\) [[_homogeneous, `class C`], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1064 |
\(a+x y'(x)^3-y(x) y'(x)^2=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 1065 |
\(x y'(x)^3+(2 x-y(x)) y'(x)^2+(2-2 y(x)) y'(x)-y(x)+1=0\) [_dAlembert] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 1066 |
\(-\left (x^2+y(x)+x\right ) y'(x)^2+\left (x^2+x y(x)+y(x)\right ) y'(x)+x y'(x)^3-x y(x)=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 1067 |
\(4 x^2+x y'(x)^3-2 y(x) y'(x)^2=0\) [[_1st_order, _with_linear_symmetries]] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1068 |
\(2 x y'(x)^3-3 y(x) y'(x)^2-x=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 1069 |
\(4 x y'(x)^3-6 y(x) y'(x)^2+3 y(x)-x=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1070 |
\(8 x y'(x)^3-12 y(x) y'(x)^2+9 y(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1071 |
\(x^2 y'(x)^3-2 x y(x) y'(x)^2+y(x)^2 y'(x)+1=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 1072 |
\(b x \left (a^2-x^2\right ) y'(x)^2+\left (a^2-x^2\right ) y'(x)^3-b x-y'(x)=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 1073 |
\(x \left (x^5+3 y(x)^2\right ) y'(x)-2 x^5 y(x)-3 x^2 y(x) y'(x)^2+x y'(x)^3-y(x)^3=0\) [`y=_G(x,y')`] Solution method Change of variable Maple ✗ |
| ODE 1074 |
\(2 x^3 y'(x)^3+6 x^2 y(x) y'(x)^2-(1-6 x y(x)) y(x) y'(x)+2 y(x)^3=0\) [[_homogeneous, `class G`]] Solution method Change of variable Maple ✓ |
| ODE 1075 |
\(8 x^3 y'(x)^3+12 x^2 y(x) y'(x)^2-\left (1-6 x y(x)^2\right ) y'(x)+y(x)^3=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 1076 |
\(x^4 y'(x)^3-x^3 y(x) y'(x)^2-x^2 y(x)^2 y'(x)+x y(x)^3=1\) [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓ |
| ODE 1077 |
\(x^6 y'(x)^3-x y'(x)-y(x)=0\) [[_1st_order, _with_linear_symmetries]] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1078 |
\(y(x) y'(x)^3-3 x y'(x)+3 y(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1079 |
\(2 y(x) y'(x)^3-3 x y'(x)+2 y(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1080 |
\(2 y(x) y'(x)^3+3 y(x) y'(x)+x=0\) [[_homogeneous, `class A`], _dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1081 |
\(2 y(x) y'(x)^3-y(x) y'(x)^2+2 x y'(x)-x=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 1082 |
\((2 y(x)+x) y'(x)^3+3 (y(x)+x) y'(x)^2+(y(x)+2 x) y'(x)=0\) [_quadrature] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 1083 |
\(y(x)^2 y'(x)^3-x y'(x)+y(x)=0\) [[_1st_order, _with_linear_symmetries]] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1084 |
\(y(x)^2 y'(x)^3+2 x y'(x)-y(x)=0\) [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓ |
| ODE 1085 |
\(4 y(x)^2 y'(x)^3-2 x y'(x)+y(x)=0\) [[_1st_order, _with_linear_symmetries]] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1086 |
\(16 y(x)^2 y'(x)^3+2 x y'(x)-y(x)=0\) [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓ |
| ODE 1087 |
\(x \left (x^2+1\right ) y'(x)-x^2 y(x)+y(x)^3 \left (-y'(x)^2\right )+x y(x)^2 y'(x)^3=0\) [`y=_G(x,y')`] Solution method Change of variable Maple ✗ |
| ODE 1088 |
\(x^7 y(x)^2 y'(x)^3+\left (1-3 x^6 y(x)^3\right ) y'(x)^2+3 x^5 y(x)^4 y'(x)-x^4 y(x)^5=0\) [[_homogeneous, `class G`]] Solution method Change of variable Maple ✓ |
| ODE 1089 |
\(y(x)^3 y'(x)^3-x y'(x)+y(x)=0\) [[_1st_order, _with_linear_symmetries]] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✗ |
| ODE 1090 |
\(x^3+3 x^2 y(x) y'(x)+y(x)^3 y'(x)^3-(1-3 x) y(x)^2 y'(x)^2-y(x)^2=0\) [`y=_G(x,y')`] Solution method Change of variable Maple ✓ |
| ODE 1091 |
\(y(x)^4 y'(x)^3-6 x y'(x)+2 y(x)=0\) [[_1st_order, _with_linear_symmetries]] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1092 |
\(y'(x)^4=(y(x)-a)^3 (y(x)-b)^2\) [_quadrature] Solution method Change of variable Maple ✓ |
| ODE 1093 |
\(f(x) (y(x)-a)^3 (y(x)-b)^2+y'(x)^4=0\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 1094 |
\(f(x) (y(x)-a)^3 (y(x)-b)^3+y'(x)^4=0\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 1095 |
\(f(x) (y(x)-a)^3 (y(x)-b)^3 (y(x)-c)^2+y'(x)^4=0\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 1096 |
\(y'(x)^4+x y'(x)-3 y(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1097 |
\(y'(x)^4-3 (1-x) y'(x)^2+3 (1-2 y(x)) y'(x)+3 x=0\) odeadvisor timed out Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 1098 |
\(-4 x^2 y(x) y'(x)^2+y'(x)^4+16 x y(x)^2 y'(x)-16 y(x)^3=0\) [[_homogeneous, `class G`]] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1099 |
\(y'(x)^4+4 y(x) y'(x)^3+6 y(x)^2 y'(x)^2-\left (1-4 y(x)^3\right ) y'(x)-y(x) \left (3-y(x)^3\right )=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Use new
variable Maple ✓ |
| ODE 1100 |
\(2 y'(x)^4-y(x) y'(x)-2=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 1101 |
\(12 x^3+x y'(x)^4-2 y(x) y'(x)^3=0\) [[_1st_order, _with_linear_symmetries]] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1102 |
\(a y'(x)^3+b y'(x)^2+y'(x)^5=c y(x)\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 1103 |
\(a y'(x)^4+b y'(x)^3+c x y'(x)^2+y'(x)^5=c y(x)\) [_dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 1104 |
\(3 y'(x)^5-y(x) y'(x)+1=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 1105 |
\(y'(x)^6=(y(x)-a)^4 (y(x)-b)^3\) [_quadrature] Solution method Change of variable Maple ✓ |
| ODE 1106 |
\(f(x) (y(x)-a)^4 (y(x)-b)^3+y'(x)^6=0\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 1107 |
\(f(x) (y(x)-a)^5 (y(x)-b)^3+y'(x)^6=0\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 1108 |
\(f(x) (y(x)-a)^5 (y(x)-b)^4+y'(x)^6=0\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 1109 |
\(f(x) (y(x)-a)^5 (y(x)-b)^4 (y(x)-c)^3+y'(x)^6=0\) [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]] Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 1110 |
\(x^2 \left (y'(x)^6+3 y(x)^4+3 y(x)^2+1\right )=a^2\) [_rational] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(x\) Maple ✗ |
| ODE 1111 |
\(y'(x)^n=a x^r+b y'(x)^s\) [_quadrature] Solution method Change of variable Maple ✓ |
| ODE 1112 |
\(y'(x)^n=f(x)^n (y(x)-a)^{n+1} (y(x)-b)^{n-1}\) [_separable] Solution method Change of variable Maple ✓ |
| ODE 1113 |
\(y'(x)^n=f(x) (y(x)-a)^{n+1}\) [_separable] Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 1114 |
\(y'(x)^n=f(x) (y(x)-a)^{n-1} (y(x)-b)^{n-1}\) [_separable] Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 1115 |
\(f(x) g(x)+y'(x)^n=0\) [_quadrature] Solution method Form \((y')^m + X(x,y)=0\) Maple ✓ |
| ODE 1116 |
\(f(x,y(x))+y'(x)^n=0\) [NONE] Solution method Form \((y')^m + X(x,y)=0\) Maple ✗ |
| ODE 1117 |
\(a y'(x)+y'(x)^n=b y(x)\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 1118 |
\(y'(x)^n+x y'(x)-y(x)=0\) [_Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 1119 |
\(a y'(x)^m+y'(x)^n=b y(x)\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 1120 |
\(\text {Y1}(y(x)) y'(x)^{n-1}+y'(x)^n=0\) [_quadrature] Solution method Form \((y')^m + f_1(x,y) (y')^{m-1} \dots + f_m(x,y)=0\) Maple ✗ |
| ODE 1121 |
\(\text {X1}(x,y(x)) y'(x)^{n-1}+y'(x)^n=0\) [_quadrature] Solution method Form \((y')^m + f_1(x,y) (y')^{m-1} \dots + f_m(x,y)=0\) Maple ✓ |
| ODE 1122 |
\(x^{n-1} y'(x)^n-n x y'(x)+y(x)=0\) [`y=_G(x,y')`] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1123 |
\(\text {X0}(x,y(x)) y'(x)^n+\text {X1}(x,y(x)) y'(x)^{n-1}=0\) [_quadrature] Solution method Form \(X_0(x,y) (y')^m + X_1 (x,y) (y')^{m-1} + \dots + X_m(x,y)=0\) Maple ✓ |
| ODE 1124 |
\(2 \sqrt {a y'(x)}+x y'(x)-y(x)=0\) [[_homogeneous, `class G`], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 1125 |
\((x-y(x)) \sqrt {y'(x)}=a \left (y'(x)+1\right )\) [[_homogeneous, `class C`], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1126 |
\(3 x y'(x)+2 (y(x)+1)^{3/2}-3 y(x)=0\) [_separable] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 1127 |
\(a y'(x)+\sqrt {y'(x)^2+1}=x\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(x\) Maple ✓ |
| ODE 1128 |
\(a y'(x)+\sqrt {y'(x)^2+1}=y(x)\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 1129 |
\(\sqrt {y'(x)^2+1}=x y'(x)\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 1130 |
\(-a y(x) y'(x)-a x+\sqrt {y'(x)^2+1}=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1131 |
\(-x y'(x)^2+\sqrt {y'(x)^2+1}+y(x)=0\) [_dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 1132 |
\(\sqrt {a^2+b^2 y'(x)^2}+x y'(x)-y(x)=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 1133 |
\(\sqrt {a c-b^2} \left (x y'(x)-y(x)\right )+\sqrt {a+2 b y'(x)+c y'(x)^2}=0\) [[_1st_order, _with_linear_symmetries], _rational, _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 1134 |
\(a \sqrt {y'(x)^2+1}+x y'(x)-y(x)=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 1135 |
\(a x \sqrt {y'(x)^2+1}+x y'(x)-y(x)=0\) [[_homogeneous, `class A`], _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1136 |
\(-a y(x) y'(x)-a x+y(x) \sqrt {y'(x)^2+1}=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1137 |
\(y(x) \sqrt {y'(x)^2+1}=f\left (y(x) y'(x)+x\right )\) [`x=_G(y,y')`] Solution method The method of Lagrange Maple ✓ |
| ODE 1138 |
\(\sqrt {\left (a x^2+y(x)^2\right ) \left (y'(x)^2+1\right )}-a x-y(x) y'(x)=0\) [[_homogeneous, `class A`], _rational, _dAlembert] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\) Maple ✓ |
| ODE 1139 |
\(a \sqrt [3]{y'(x)^3+1}+x y'(x)-y(x)=0\) [_Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 1140 |
\(y'(x) \left (a+x \sqrt {y'(x)^2+1}\right )=y(x) \sqrt {y'(x)^2+1}\) [_Clairaut] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 1141 |
\(x y'(x)+\cos \left (y'(x)\right )=y(x)\) [_Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 1142 |
\(a \cos \left (y'(x)\right )+b y'(x)+x=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(x\) Maple ✓ |
| ODE 1143 |
\(y'(x)+\sin \left (y'(x)\right )=x\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(x\) Maple ✓ |
| ODE 1144 |
\(y'(x) \sin \left (y'(x)\right )+\cos \left (y'(x)\right )=y(x)\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 1145 |
\(y'(x)^2 \sin \left (y'(x)\right )=y(x)\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 1146 |
\(y'(x)^2 \left (\sin \left (y'(x)\right )+x\right )=y(x)\) [_dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1147 |
\(\left (y'(x)^2+1\right ) \sin ^2\left (y(x)-x y'(x)\right )=1\) [_Clairaut] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 1148 |
\(-\sqrt {1-y'(x)^2}+y'(x) \left (\cos ^{-1}\left (y'(x)\right )-x\right )+y(x)=0\) [_Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 1149 |
\(\left (y'(x)^2+1\right ) \left (a x+\tan ^{-1}\left (y'(x)\right )\right )+y'(x)=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(x\) Maple ✓ |
| ODE 1150 |
\(-y'(x)^2+e^{y'(x)-y(x)}+1=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 1151 |
\(y'(x)+\log \left (y'(x)\right )=x\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(x\) Maple ✓ |
| ODE 1152 |
\(a+x y'(x)+\log \left (y'(x)\right )=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(x\) Maple ✓ |
| ODE 1153 |
\(a+x y'(x)+\log \left (y'(x)\right )=y(x)\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 1154 |
\(a+b y(x)+x y'(x)+\log \left (y'(x)\right )=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 1155 |
\(4 x y'(x)+\log \left (y'(x)\right )-2 y(x)=0\) [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 1156 |
\(a \left (x y'(x)-y(x)\right )+\log \left (y'(x)\right )=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 1157 |
\(a \left (\log \left (y'(x)\right )-y'(x)\right )+y(x)-x=0\) [[_homogeneous, `class C`], _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 1158 |
\(y'(x)+y(x) \log \left (y'(x)\right )-x y(x)-y(x) \log (y(x))=0\) [_separable] Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 1159 |
\(-(x+1) y'(x)+y'(x) \log \left (y'(x)\right )+y(x)=0\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 1160 |
\(\log \left (x y'(x)-y(x)\right )=y'(x)\) [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1161 |
\(y'(x) \log \left (\sqrt {a+y'(x)^2}+y'(x)\right )-x y'(x)-\sqrt {y'(x)^2+1}+y(x)=0\) [_Clairaut] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 1162 |
\(y'(x) \tan \left (y'(x)\right )+\log \left (\cos \left (y'(x)\right )\right )=y(x)\) [_dAlembert] Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 1163 |
\(f\left (y'(x)\right )=0\) [_quadrature] Solution method Missing Variables ODE, Both independent and dependent
variable missing Maple ✓ |
| ODE 1164 |
\(f\left (x,y'(x)\right )=0\) [_quadrature] Solution method Missing Variables ODE, Dependent variable missing Maple ✓ |
| ODE 1165 |
\(f\left (x y'(x)^2\right )=y(x)-2 x y'(x)\) [`y=_G(x,y')`] Solution method Change of variable Maple ✓ |
| ODE 1166 |
\(f\left (y(x),y'(x)\right )=0\) [_quadrature] Solution method Missing Variables ODE, Independent variable missing Maple ✓ |
| ODE 1167 |
\(f\left (y'(x)\right )+x y'(x)=y(x)\) [_Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 1168 |
\(f\left (y'(x)\right )+x g\left (y'(x)\right )=y(x)\) [_dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 1169 |
\(f\left (y'(x),y(x)-x y'(x)\right )=0\) [_Clairaut] Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 1170 |
\(f\left (x y'(x),y(x)\right )=0\) [_separable] Solution method Homogeneous ODE, The Isobaric equation Maple ✓ |
| ODE 1171 |
\(x^n f\left (y'(x),\frac {y(x)}{x}\right )=0\) [[_homogeneous, `class A`], _dAlembert] Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\) Maple ✓ |
| ODE 1172 |
\(f\left (y(x) y'(x)+x\right )=y(x)^2 \left (y'(x)^2+1\right )\) [`x=_G(y,y')`] Solution method Change of variable Maple ✓ |
| ODE 1173 |
\(y(x) f\left (\frac {y'(x)}{y(x)},x\right )=0\) [_separable] Solution method Homogeneous ODE, equation of form \(y f(x , \frac {y'}{y})\) Maple ✓ |
| ODE 1174 |
\(f\left (x,y(x),y'(x)\right )=0\) [NONE] Solution method No Missing Variables ODE Maple ✗ |
| ODE 1175 |
\(y''(x)=0\) [[_2nd_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 1176 |
\(y''(x)=x+\sin (x)\) [[_2nd_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 1177 |
\(y''(x)=\text {c1} \cos (a x)+\text {c2} \sin (b x)\) [[_2nd_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 1178 |
\(y''(x)=e^x x\) [[_2nd_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 1179 |
\(y''(x)=\text {c1} e^{a x}+\text {c2} e^{-b x}\) [[_2nd_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 1180 |
\(y''(x)+y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1181 |
\(y''(x)-y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1182 |
\(y''(x)+y(x)=a x\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1183 |
\(y''(x)+y(x)=a \cos (b x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1184 |
\(y''(x)+y(x)=8 \cos (x) \cos (2 x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1185 |
\(y''(x)+y(x)=\sec (x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1186 |
\(y''(x)+y(x)=a \sin (b x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1187 |
\(y''(x)+y(x)=\sin (a x) \sin (b x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1188 |
\(y''(x)+y(x)=4 x \sin (x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1189 |
\(y''(x)+y(x)=x (\cos (x)-x \sin (x))\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1190 |
\(y''(x)+y(x)=\tan ^2(x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1191 |
\(y''(x)+y(x)=e^{-x}\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1192 |
\(y''(x)+y(x)=e^x \left (x^2-1\right )\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1193 |
\(y''(x)+y(x)=e^x \sin (2 x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1194 |
\(y''(x)+y(x)=e^{2 x} \cos (x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1195 |
\(y''(x)-2 y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1196 |
\(y''(x)-2 y(x)=4 e^{x^2} x^2\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1197 |
\(y''(x)+4 y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1198 |
\(y''(x)+4 y(x)=x \sin ^2(x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1199 |
\(y''(x)+4 y(x)=2 \tan (x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1200 |
\(y''(x)+4 y(x)=2 \tan (x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1201 |
\(y''(x)-a^2 y(x)=x+1\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1202 |
\(y''(x)=a x+b y(x)\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1203 |
\(a^2 y(x)+y''(x)=x^2+x+1\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1204 |
\(a^2 y(x)+y''(x)=\cos (b x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1205 |
\(a^2 y(x)+y''(x)=\cot (a x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1206 |
\(a^2 y(x)+y''(x)=\sin (b x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1207 |
\(y''(x)+x y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1208 |
\(y(x) (a+b x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1209 |
\(\left (a+x^2\right ) y(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1210 |
\(\left (a-x^2\right ) y(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1211 |
\(y''(x)=\left (a+x^2\right ) y(x)\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1212 |
\(y(x) \left (a+b^2 x^2\right )+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1213 |
\(y(x) \left (a+b x+c x^2\right )+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1214 |
\(y(x) \left (\text {a0}+\text {a1} x^2+x^4\right )+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1215 |
\(a x^k y(x)+y''(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1216 |
\(y(x) \left (\sum _{n=0}^m a(n) x^n\right )+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1217 |
\(y(x) (a+b \cos (2 x))+y''(x)=0\) [_ellipsoidal] Solution method TO DO Maple ✓ |
| ODE 1218 |
\(y(x) (a+b \cos (2 x)+k \cos (4 x))+y''(x)=0\) [_ellipsoidal] Solution method TO DO Maple ✓ |
| ODE 1219 |
\(y(x) \left (\sum _{n=0}^m a(n) \cos (2 n x)\right )+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1220 |
\(y''(x)=2 y(x) \csc ^2(x)\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1221 |
\(a y(x) \csc ^2(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1222 |
\(y(x) \left (\text {a0}+\text {a1} \cos ^2(x)+\text {a2} \csc ^2(x)\right )+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1223 |
\(y''(x)=y(x) \left (a^2+(p-1) p \csc ^2(x)+(q-1) q \sec ^2(x)\right )\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1224 |
\(y(x) \left (a+b \sin ^2(x)\right )+y''(x)=0\) [_ellipsoidal] Solution method TO DO Maple ✓ |
| ODE 1225 |
\(y''(x)=y(x) \left (2 \tan ^2(x)+1\right )\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1226 |
\(y''(x)-y(x) \left (a^2-b e^x\right )=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1227 |
\(y''(x)-\left (a^2-e^{2 x}\right ) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1228 |
\(y(x) \left (a+b e^x+c e^{2 x}\right )+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1229 |
\(a e^{b x} y(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1230 |
\(y(x) \left (a+b \cosh ^2(x)\right )+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1231 |
\(y(x) \left (a+b \sinh ^2(x)\right )+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1232 |
\(y(x) \left (a+b \sin ^2(x)\right )+y''(x)=0\) [_ellipsoidal] Solution method TO DO Maple ✓ |
| ODE 1233 |
\(\frac {(a+b) y(x)}{x^2}+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1234 |
\(y''(x)-y'(x)+x y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1235 |
\(y''(x)+2 y'(x)+y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1236 |
\(y''(x)-2 y'(x)+y(x)=(x-6) x^2\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1237 |
\(y''(x)-2 y'(x)+y(x)=e^x\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1238 |
\(y''(x)-2 y'(x)+y(x)=e^x \left (3 x^2+2 x+1\right )\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1239 |
\(y''(x)-2 y'(x)+y(x)=e^x \sin (x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1240 |
\(y''(x)+2 y'(x)+y(x)=x^2+3 e^{2 x}-\cos (x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1241 |
\(y''(x)-2 y'(x)+y(x)=8 e^{3 x} x^2\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1242 |
\(y''(x)-2 y'(x)+y(x)=50 \cos (x) \cosh (x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1243 |
\(y''(x)+2 y'(x)+3 y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1244 |
\(y''(x)+2 y'(x)+y(x)=e^{-x} \cos (x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1245 |
\(y''(x)+2 y'(x)+5 y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1246 |
\(y''(x)+2 y'(x)+5 y(x)=8 \sinh (x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1247 |
\(-2 \tan (a) y'(x)+\csc ^2(a) y(x)+y''(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1248 |
\(-2 \tan (a) y'(x)+\csc ^2(a) y(x)+y''(x)=x^2 e^{x \tan (a)}\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1249 |
\(y''(x)+3 y'(x)+2 y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1250 |
\(y''(x)+3 y'(x)+2 y(x)=\cos (a x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1251 |
\(y''(x)+3 y'(x)+2 y(x)=e^x+\sin (x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1252 |
\(y''(x)-3 y'(x)+2 y(x)=x^2+2 e^{-x}\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1253 |
\(y''(x)-3 y'(x)+2 y(x)=x e^{a x}\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1254 |
\(y''(x)-3 y'(x)-4 y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1255 |
\(y''(x)-3 y'(x)-4 y(x)=10 \cos (2 x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1256 |
\(y''(x)-4 y'(x)+4 y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1257 |
\(y''(x)-4 y'(x)+4 y(x)=e^{2 x} \cos ^2(x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1258 |
\(y''(x)+4 y'(x)+5 y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1259 |
\(y''(x)+4 y'(x)+5 y(x)=\sin (x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1260 |
\(y''(x)-4 y'(x)+13 y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1261 |
\(y''(x)-5 y'(x)+6 y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1262 |
\(y''(x)-5 y'(x)+6 y(x)=4 e^x x^2\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1263 |
\(y''(x)-5 y'(x)+6 y(x)=e^{a x}\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1264 |
\(y''(x)+6 y'(x)+9 y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1265 |
\(y''(x)+6 y'(x)+9 y(x)=e^{-3 x} \cosh (x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1266 |
\(y''(x)-7 y'(x)+12 y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1267 |
\(y''(x)-7 y'(x)+12 y(x)=x\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1268 |
\(y''(x)+8 y'(x)+16 y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1269 |
\(y''(x)+8 y'(x)+16 y(x)=4 e^x-e^{2 x}\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1270 |
\(y''(x)-9 y'(x)+20 y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1271 |
\(y''(x)-9 y'(x)+20 y(x)=e^{3 x} x^2\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1272 |
\(2 a y'(x)+b^2 y(x)+y''(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1273 |
\(2 a y'(x)+b^2 y(x)+y''(x)=c \sin (k x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1274 |
\(a^2 y(x)-2 a y'(x)+y''(x)=e^x\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1275 |
\(\left (a^2+b^2\right )^2 y(x)-4 a b y'(x)+y''(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1276 |
\(a y'(x)+b y(x)+y''(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1277 |
\(a y'(x)+b y(x)+y''(x)=f(x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1278 |
\(a y'(x)+y(x) (b+c x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1279 |
\(a y'(x)+y(x) \left (b+c x^2\right )+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1280 |
\(a y'(x)+y(x) \left (b+c e^x\right )+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1281 |
\(b e^{2 a x} y(x)+a y'(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1282 |
\(a y'(x)+b e^{k x} y(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1283 |
\(y''(x)+x y'(x)+y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1284 |
\(y''(x)+x y'(x)-y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1285 |
\(y''(x)-x y'(x)+2 y(x)=0\) [_Hermite] Solution method TO DO Maple ✓ |
| ODE 1286 |
\(n y(x)+y''(x)-x y'(x)=0\) [_Hermite] Solution method TO DO Maple ✓ |
| ODE 1287 |
\(-a y(x)+y''(x)-x y'(x)=0\) [_Hermite] Solution method TO DO Maple ✓ |
| ODE 1288 |
\(y''(x)-x y'(x)-((1-x) y(x))=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1289 |
\(y''(x)-2 x y'(x)+6 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1290 |
\(y''(x)+2 x y'(x)-8 y(x)=0\) [_erf] Solution method TO DO Maple ✓ |
| ODE 1291 |
\(2 n y(x)+y''(x)-2 x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1292 |
\(-\left (\left (-x^2-x+1\right ) y(x)\right )+y''(x)-(2 x+1) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1293 |
\(2 \left (2 x^2+1\right ) y(x)+y''(x)+4 x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1294 |
\(-\left (\left (3-4 x^2\right ) y(x)\right )+y''(x)-4 x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1295 |
\(-\left (\left (3-4 x^2\right ) y(x)\right )+y''(x)-4 x y'(x)=e^{x^2}\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1296 |
\(a^2 x^2 y(x)-2 a x y'(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1297 |
\(a x y'(x)+b y(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1298 |
\((a+b x) y'(x)+c y(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1299 |
\((\text {a0}+\text {b0} x) y'(x)+y(x) (\text {a1}+\text {b1} x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1300 |
\((\text {a0}+\text {b0} x) y'(x)+y(x) \left (\text {a1}+\text {b1} x+\text {c1} x^2\right )+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1301 |
\(-2 a \left (1-2 a x^2\right ) y(x)-4 a x y'(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1302 |
\(x^2 \left (-y'(x)\right )+y''(x)+x y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1303 |
\(x^2 \left (-y'(x)\right )+y''(x)+x y(x)=x\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1304 |
\(x^2 y'(x)+y''(x)-4 x y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1305 |
\(x^4 y'(x)-x^3 y(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1306 |
\(a (k+1) x^{k-1} y(x)+a x^k y'(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1307 |
\(a k x^{k-1} y(x)+a x^k y'(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1308 |
\(-a x^{k-1} y(x)+a x^k y'(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1309 |
\(a x^k y'(x)+b x^{k-1} y(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1310 |
\(y''(x)-\cot (x) y'(x)+2 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1311 |
\(k (k+1) y(x)+y''(x)+\cot (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1312 |
\(y''(x)+\cot (x) y'(x)-y(x) \csc ^2(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1313 |
\(y(x) \left (p (p+1)-k^2 \csc ^2(x)\right )+y''(x)+\cot (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1314 |
\(y(x) \left (\text {a0}+4 \text {a1} \sin ^2(x)-\text {a2} \csc ^2(x)\right )+y''(x)+\cot (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1315 |
\(y''(x)+2 \cot (x) y'(x)+3 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1316 |
\(y''(x)+2 \cot (x) y'(x)+3 y(x)=e^x \csc (x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1317 |
\(a \cot (x) y'(x)+y(x) \left (b+k^2 \cos ^2(x)\right )+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1318 |
\(y(x) \left (a \cot ^2(x)+b \cot (x) \csc (x)+c \csc ^2(x)\right )+k \cot (x) y'(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1319 |
\(y''(x)-\cot (2 x) y'(x)+2 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1320 |
\(a y(x) \tan ^2(x)+y''(x)-2 \cot (2 x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1321 |
\(a \cot (b x) y'(x)+c y(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1322 |
\(\left (b^2-a^2\right ) y(x)+2 a \cot (a x) y'(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1323 |
\(a y(x) \tan ^2\left (\frac {x}{2}\right )+y''(x)-\csc (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1324 |
\(y''(x)+y'(x) (\cot (x)+\csc (x))=a \csc (x)+1\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1325 |
\(y''(x)-\csc (2 x) y'(x)+y(x) \left (\sin ^2(x)+2\right ) \csc ^2(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1326 |
\(a y(x) \csc ^2(x)+y''(x)+(\cos (x)+2) \csc (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1327 |
\(y''(x)-(3 \cos (x)+2) \csc (x) y'(x)-2 y(x) (\cos (x)+1) \sec (x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1328 |
\(y''(x)-y'(x) (\cot (x)-\sin (x))+y(x) \sin ^2(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1329 |
\(y''(x)-\sin (x) y'(x)+y(x) (-\cos (x))=a-x+x \log (x)\) [[_2nd_order, _exact, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1330 |
\(-2 \csc (2 x) \left (1-a \sin ^2(x)\right ) y'(x)+b y(x) \tan ^2(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1331 |
\(a y(x) \cos ^2(x)+y''(x)+\tan (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1332 |
\(a y(x) \cot ^2(x)+y''(x)+\tan (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1333 |
\(-a (a+1) y(x) \csc ^2(x)+y''(x)-\tan (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1334 |
\(y(x) \left (a \cos ^2(x)-\sec ^2(x)\right )+y''(x)-\tan (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1335 |
\(y''(x)+2 \tan (x) y'(x)-y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1336 |
\(y''(x)+2 \tan (x) y'(x)-y(x)=(x+1) \sec (x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1337 |
\(y''(x)+2 \tan (x) y'(x)+3 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1338 |
\(b y(x)+y''(x)-2 \tan (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1339 |
\(-\left (\left (a^2+1\right ) y(x)\right )+y''(x)-2 \tan (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1340 |
\(-\left (\left (a^2+1\right ) y(x)\right )+y''(x)-2 \tan (x) y'(x)=\sin (x)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1341 |
\(a \tan (x) y'(x)+b y(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1342 |
\(y''(x)-\left (2 e^x+1\right ) y'(x)+e^{2 x} y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1343 |
\(y(x) \left (\text {a0}+4 \text {a1} \sinh ^2(x)-\text {a2} \text {csch}^2(x)\right )+y''(x)+\coth (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1344 |
\(y(x) \left (\text {a0}+4 \text {a1} \cosh ^2(x)-\text {a2} \text {sech}^2(x)\right )+y''(x)+\tanh (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1345 |
\(b y(x)+y''(x)+2 \tanh (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1346 |
\(a \tanh (x) y'(x)+b y(x)+y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1347 |
\(f(x) y'(x)+y''(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1348 |
\(a k x^{k-1} y(x)+2 a x^k y'(x)+2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1349 |
\(3 y''(x)-10 y'(x)+3 y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1350 |
\(4 y''(x)=\left (a+x^2\right ) y(x)\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1351 |
\(\left (4 a-x^2+2\right ) y(x)+4 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1352 |
\(4 y''(x)-8 y'(x)+3 y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1353 |
\(x y''(x)+y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1354 |
\((a+x) y(x)+x y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1355 |
\(x y''(x)+y'(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1356 |
\(x y''(x)+y'(x)=x^n\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1357 |
\(x y''(x)+y'(x)-y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1358 |
\(x y''(x)+y'(x)-((x+1) y(x))=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1359 |
\(4 x^3 y(x)+x y''(x)-y'(x)=0\) [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1360 |
\(-a^2 x^3 y(x)+x y''(x)-y'(x)=0\) [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1361 |
\(x^3 \left (e^{x^2}-k^2\right ) y(x)+x y''(x)-y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1362 |
\(x y''(x)+2 y'(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1363 |
\(x y''(x)+2 y'(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1364 |
\(x y''(x)+2 y'(x)-x y(x)=e^x\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1365 |
\(a x y(x)+x y''(x)+2 y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1366 |
\(a x^2 y(x)+x y''(x)+2 y'(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1367 |
\(a y'(x)+x y''(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1368 |
\((a+1) y'(x)+x y''(x)+y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1369 |
\((1-a) y'(x)+x y''(x)+y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1370 |
\((a+1) y'(x)+x y''(x)-y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1371 |
\(2 n y'(x)+x y''(x)-y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1372 |
\(a y'(x)+b y(x)+x y''(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1373 |
\(a y'(x)+b x y(x)+x y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1374 |
\(a y'(x)+y(x) (\text {b1}+\text {b2} x)+x y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1375 |
\(a y'(x)+y(x) \left (\text {a1}+\text {b1} x+\text {c1} x^2\right )+x y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1376 |
\(a y'(x)+b x^k y(x)+x y''(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1377 |
\(x y''(x)-(x+1) y'(x)+y(x)=0\) [_Laguerre] Solution method TO DO Maple ✓ |
| ODE 1378 |
\(n y(x)+x y''(x)+(1-x) y'(x)=0\) [_Laguerre] Solution method TO DO Maple ✓ |
| ODE 1379 |
\((k-x+1) y'(x)+n y(x)+x y''(x)=0\) [_Laguerre] Solution method TO DO Maple ✓ |
| ODE 1380 |
\(x y''(x)-(x+1) y'(x)+2 (1-x) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1381 |
\(x y''(x)-(2-x) y'(x)-y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1382 |
\(x y''(x)-(x+3) y'(x)+y(x)=0\) [_Laguerre] Solution method TO DO Maple ✓ |
| ODE 1383 |
\(x y''(x)-(x+3) y'(x)+3 y(x)=0\) [_Laguerre] Solution method TO DO Maple ✓ |
| ODE 1384 |
\((a+x) y'(x)+b y(x)+x y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1385 |
\(-a y(x)+(c-x) y'(x)+x y''(x)=0\) [_Laguerre] Solution method TO DO Maple ✓ |
| ODE 1386 |
\(x y''(x)+(1-2 x) y'(x)-((1-x) y(x))=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1387 |
\(x y''(x)-(2 x+1) y'(x)+(x+1) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1388 |
\(x y''(x)-(2 x+1) y'(x)+(x+1) y(x)=x^2-x-1\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1389 |
\((a+b x) y'(x)+c y(x)+x y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1390 |
\((\text {a1}+\text {b1} x) y'(x)+y(x) (\text {a2}+\text {b2} x)+x y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1391 |
\(-2 (a+b x) y'(x)+y(x) (2 a+b x)+x y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1392 |
\(y'(x) (x (a+b)+m+n)+y(x) (a b x+a n+b m)+x y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1393 |
\(x y''(x)-\left (1-x^2\right ) y'(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1394 |
\(-\left (4-x^2\right ) y'(x)+x y''(x)+2 x y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1395 |
\(x^3 y(x)-\left (2 x^2+1\right ) y'(x)+x y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1396 |
\(-8 x^3 y(x)-\left (2 x^2+1\right ) y'(x)+x y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1397 |
\(-8 x^3 y(x)-\left (2 x^2+1\right ) y'(x)+x y''(x)=4 e^{-x^2} x^3\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1398 |
\(\left (4 x^2+1\right ) y'(x)+4 x \left (x^2+1\right ) y(x)+x y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1399 |
\(-\left (1-2 a x^3\right ) y'(x)+a x^2 \left (a x^3+1\right ) y(x)+x y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1400 |
\((x f(x)+2) y'(x)+f(x) y(x)+x y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1401 |
\((1-x) y''(x)+x y'(x)-y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1402 |
\((1-x) y''(x)+x y'(x)-y(x)=(1-x)^2\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1403 |
\((3-x) y''(x)-(9-4 x) y'(x)+3 (2-x) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1404 |
\((a-x) y''(x)-2 y'(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1405 |
\((a+x) y''(x)+(\text {a1}+\text {b1} x) y'(x)+y(x) (\text {a2}+\text {b2} x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1406 |
\(2 x y''(x)+y'(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1407 |
\(a y(x)+2 x y''(x)+y'(x)=0\) [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1408 |
\(-a y(x)+2 x y''(x)+y'(x)=0\) [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1409 |
\(y(x) (a+b x)+2 x y''(x)+y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1410 |
\(-\left (2 x^2+1\right ) y'(x)+2 x y''(x)-x y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1411 |
\((1-2 x) y''(x)-(x+2) y'(x)-y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1412 |
\((1-2 x) y''(x)-(4-3 x) y'(x)+(3-x) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1413 |
\(4 y''(x)+2 y'(x)+y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1414 |
\(4 y''(x)-2 y'(x)-y(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1415 |
\(4 x y''(x)+4 \coth (x) y'(x)+y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✗ |
| ODE 1416 |
\(y(x) (a+b x)+16 x y''(x)+8 y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1417 |
\((a+b x) y''(x)+c y'(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1418 |
\((\text {a0}+\text {b0} x) y''(x)+(\text {a1}+\text {b1} x) y'(x)+y(x) (\text {a2}+\text {b2} x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1419 |
\((1-x \cot (x)) y''(x)-x y'(x)+y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1420 |
\(x^2 y''(x)=a+b x\) [[_2nd_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 1421 |
\(x^2 y''(x)=2 y(x)\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1422 |
\(x^2 y''(x)=6 y(x)\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1423 |
\(x^2 y''(x)=12 y(x)\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1424 |
\(a y(x)+x^2 y''(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1425 |
\(y(x) (a+b x)+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1426 |
\(x^2 y''(x)-\left (2-x^2\right ) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1427 |
\(x^2 y''(x)-\left (2-x^2\right ) y(x)=x^4\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1428 |
\(x^2 y''(x)-\left (a^2 x^2+2\right ) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1429 |
\(x^2 y''(x)-\left (6-a^2 x^2\right ) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1430 |
\(x^2 y''(x)-y(x) \left (a^2 x^2+n (n+1)\right )=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1431 |
\(x^2 y''(x)-y(x) \left ((n-1) n-a^2 x^2\right )=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1432 |
\(y(x) \left (a+b x+c x^2\right )+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1433 |
\(x^2 y''(x)-y(x) \left ((a-1) a-b x^k\right )=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1434 |
\(x^k y(x) \left (a+b x^k\right )+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1435 |
\(-b y(x) \left (a+b x^2\right )+a y'(x)+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1436 |
\(x^2 y''(x)+x y'(x)+y(x)=0\) [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1437 |
\(x^2 y''(x)+x y'(x)-y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1438 |
\(x^2 y''(x)-x y'(x)+y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1439 |
\(x^2 y''(x)+x y'(x)-y(x)=a x^2\) [[_2nd_order, _exact, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1440 |
\(x^2 y''(x)-x y'(x)+y(x)=x^2 (x+3)\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1441 |
\(x^2 y''(x)-x y'(x)+y(x)=3 x^3\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1442 |
\(x^2 y''(x)+x y'(x)+y(x)=\log (x)\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1443 |
\(x^2 y''(x)-x y'(x)+2 y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1444 |
\(x^2 y''(x)-x y'(x)+2 y(x)=x \log (x)\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1445 |
\(x^2 y''(x)-x y'(x)-3 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1446 |
\(a^2 (-y(x))+x^2 y''(x)+x y'(x)=0\) [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1447 |
\(y(x) (a+b x)+x^2 y''(x)+x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1448 |
\(-\left (p^2-x^2\right ) y(x)+x^2 y''(x)+x y'(x)=0\) [_Bessel] Solution method TO DO Maple ✓ |
| ODE 1449 |
\(-\left (p^2+x^2\right ) y(x)+x^2 y''(x)+x y'(x)=0\) [[_Bessel, _modified]] Solution method TO DO Maple ✓ |
| ODE 1450 |
\(-\left (p^2+i x^2\right ) y(x)+x^2 y''(x)+x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1451 |
\(-y(x) \left (p^2-a^2 x^2\right )+x^2 y''(x)+x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1452 |
\(-y(x) \left (a+b x+c x^2\right )+x^2 y''(x)+x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1453 |
\(-y(x) \left (4 a x^2+n^2-x^4\right )+x^2 y''(x)+x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1454 |
\(-y(x) \left (a^2+b^2 x^2+c^2 x^4\right )+x^2 y''(x)+x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1455 |
\((m+1) a(m) x^m y(x)+x^2 y''(x)+x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1456 |
\((a+x) y'(x)+x^2 y''(x)-y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1457 |
\(x^2 y''(x)-2 x y'(x)+2 y(x)=0\) [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1458 |
\(x^2 y''(x)-2 x y'(x)+2 y(x)=4 x^3\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1459 |
\(x^2 y''(x)-2 x y'(x)+2 y(x)=x^3 \sin (x)\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1460 |
\(x^2 y''(x)-2 x y'(x)+2 y(x)=2 x \log (x)\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1461 |
\(x^2 y''(x)-2 x y'(x)+2 y(x)=x^5 \log (x)\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1462 |
\(x^2 y''(x)+2 x y'(x)-6 y(x)=0\) [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1463 |
\(x^2 y''(x)+2 x y'(x)-6 y(x)=2-x\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1464 |
\(\left (a^2 x^2+2\right ) y(x)+x^2 y''(x)-2 x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1465 |
\(-y(x) \left (n (n+1)-a^2 x^2\right )+x^2 y''(x)+2 x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1466 |
\(y(x) \left (a+b x^2\right )+x^2 y''(x)+2 x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1467 |
\(a y(x)+x^2 y''(x)-2 (1-x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1468 |
\(x^2 y''(x)+3 x y'(x)+y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1469 |
\(x^2 y''(x)+3 x y'(x)+y(x)=x\) [[_2nd_order, _exact, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1470 |
\(x^2 y''(x)+3 x y'(x)+y(x)=a-x+x \log (x)\) [[_2nd_order, _exact, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1471 |
\(x^2 y''(x)-3 x y'(x)+4 y(x)=0\) [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1472 |
\(x^2 y''(x)-3 x y'(x)+4 y(x)=5 x\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1473 |
\(x^2 y''(x)-3 x y'(x)-5 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1474 |
\(x^2 y''(x)-3 x y'(x)-5 y(x)=x^2 \log (x)\) [[_2nd_order, _exact, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1475 |
\(x^2 y''(x)+4 x y'(x)+2 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1476 |
\(x^2 y''(x)+4 x y'(x)+2 y(x)=e^x\) [[_2nd_order, _exact, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1477 |
\(x^2 y''(x)+4 x y'(x)+2 y(x)=\log (x+1)\) [[_2nd_order, _exact, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1478 |
\(x^2 y''(x)-4 x y'(x)+6 y(x)=0\) [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1479 |
\(x^2 y''(x)-4 x y'(x)+6 y(x)=x^2 \left (x^2-1\right )\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1480 |
\(x^2 y''(x)+\left (2-x^2\right ) y(x)+4 x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1481 |
\(x^2 y''(x)+\left (x^2+6\right ) y(x)+4 x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1482 |
\(x^2 y''(x)+5 x y'(x)+13 y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1483 |
\(x^2 y''(x)-7 x y'(x)+16 y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1484 |
\(y(x) \left (a (a+1)+b^2 x^2\right )-2 a x y'(x)+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1485 |
\(\text {a1} x y'(x)+\text {a2} y(x)+x^2 y''(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1486 |
\(\text {a1} x y'(x)+y(x) (\text {a2}+\text {b2} x)+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1487 |
\(\text {a1} x y'(x)+y(x) \left (\text {a2}+\text {b2} x^2\right )+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1488 |
\(\text {a1} x y'(x)+y(x) \left (\text {a2}+\text {b2} x+\text {c2} x^2\right )+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1489 |
\(a x y'(x)+y(x) \left (b+c x^3\right )+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1490 |
\(a x y'(x)+x^2 y(x) \left (\text {a1}+\text {b1} x^2\right )+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1491 |
\(a x y'(x)+y(x) \left (b+c x^{2 k}\right )+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1492 |
\((a+b x) y'(x)+c y(x)+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1493 |
\(-2 a x y'(x)+a (a+1) y(x)+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1494 |
\(-2 a x y'(x)+a (a+1) y(x)+x^2 y''(x)=e^x x^{a+2}\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1495 |
\(y(x) \left (a (a+1)+b^2 x^2\right )-2 a x y'(x)+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1496 |
\(y(x) (a+b x)+2 a x y'(x)+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1497 |
\(x^2 y''(x)-x^2 y'(x)-2 x^2 y(x)=2 x^2 \log (x)+x+1\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1498 |
\(y(x) \left (a+b x^2\right )+x^2 y''(x)+x^2 y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1499 |
\(x^2 y''(x)-\left (1-x^2\right ) y'(x)-y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1500 |
\(x^2 y''(x)+(1-x) x y'(x)-(1-x) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1501 |
\(x^2 y''(x)-(x+2) x y'(x)+(x+2) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1502 |
\(x^2 y''(x)-(x+2) x y'(x)+(x+2) y(x)=x^3\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1503 |
\(x^2 y''(x)+(2-x) x y'(x)-(3 x+2) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1504 |
\(x^2 y''(x)+(x+3) x y'(x)-y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1505 |
\(x^2 y''(x)-2 (x+1) x y'(x)+2 (x+1) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1506 |
\(a x^2 y'(x)+x^2 y''(x)-2 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1507 |
\(-x (a x+5) y'(x)+(3 a x+5) y(x)+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1508 |
\(x (\text {a1}+\text {b1} x) y'(x)+y(x) \left (\text {a2}+\text {b2} x+\text {c2} x^2\right )+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1509 |
\(x^3 y'(x)+x^2 y''(x)-\left (2-x^2\right ) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1510 |
\(x^2 y''(x)+\left (1-x^2\right ) x y'(x)-\left (x^2+1\right ) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1511 |
\(4 x^3 y'(x)+x^2 y''(x)+\left (4 x^4+2 x^2+1\right ) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1512 |
\(x y'(x) \left (\text {a0}+\text {b0} x^k\right )+y(x) \left (\text {a1}+\text {b1} x^k+\text {c1} x^{2 k}\right )+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1513 |
\(x y'(x) \left (\text {a0}+\text {a1} x^r+\text {a2} x^s\right )+y(x) \left (\text {b0}+\text {b1} x^r+\text {b2} x^{2 r}+\text {b3} x^s+\text {b4} x^{2 s}+\text {b5} x^{r+s}\right )+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1514 |
\(a y(x)+x^2 y''(x)+2 x^2 \cot (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1515 |
\(-y(x) (a-x \cot (x))+x^2 y''(x)+x (2 x \cot (x)+1) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1516 |
\(a y(x)+x^2 y''(x)-2 x^2 \tan (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1517 |
\(-y(x) (a+x \tan (x))+x^2 y''(x)+x (1-2 x \tan (x)) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1518 |
\(y(x) \left (f(x) \left (\text {a1}+\text {b1} x^k-1\right )+\text {a2}+\text {b2} x^k+\text {c2} x^{2 k}+f'(x)+f(x)^2\right )+x y'(x) \left (\text {a1}+\text {b1} x^k+2 f(x)\right )+x^2 y''(x)=0\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 1519 |
\(\left (x^2+1\right ) y''(x)-2 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1520 |
\(a+\left (x^2+1\right ) y''(x)-x y'(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1521 |
\(\left (1-x^2\right ) y''(x)+x y'(x)=x\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1522 |
\(\left (x^2+1\right ) y''(x)-x y'(x)+y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1523 |
\(\left (1-x^2\right ) y''(x)+x y'(x)-y(x)=0\) [_Gegenbauer] Solution method TO DO Maple ✓ |
| ODE 1524 |
\(\left (1-x^2\right ) y''(x)-x y'(x)+y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1525 |
\(\left (1-x^2\right ) y''(x)-x y'(x)-y(x)=0\) [_Gegenbauer, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1526 |
\(\left (1-x^2\right ) y''(x)+x y'(x)-y(x)=x \left (1-x^2\right )^{3/2}\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1527 |
\(\left (1-x^2\right ) y''(x)+x y'(x)+3 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1528 |
\(\left (x^2+1\right ) y''(x)+x y'(x)-4 y(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1529 |
\(\left (x^2+1\right ) y''(x)+x y'(x)-4 y(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1530 |
\(n^2 y(x)+\left (1-x^2\right ) y''(x)-x y'(x)=0\) [_Gegenbauer, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1531 |
\(a^2 y(x)+\left (x^2+1\right ) y''(x)+x y'(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1532 |
\(a^2 y(x)+\left (1-x^2\right ) y''(x)-x y'(x)=0\) [_Gegenbauer, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1533 |
\(y(x) \left (a+b x^2\right )+\left (1-x^2\right ) y''(x)-x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1534 |
\(y(x) \left (\sum _{m=0}^n a(m) x^{2 m}\right )+\left (1-x^2\right ) y''(x)-x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1535 |
\(\left (1-x^2\right ) y''(x)-2 x y'(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1536 |
\(a+\left (1-x^2\right ) y''(x)-2 x y'(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1537 |
\(\left (x^2+1\right ) y''(x)+2 x y'(x)-2 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1538 |
\(\left (x^2+1\right ) y''(x)-2 x y'(x)+2 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1539 |
\(\left (1-x^2\right ) y''(x)+2 x y'(x)-2 y(x)=\left (1-x^2\right )^2\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1540 |
\(n (n+1) y(x)+\left (1-x^2\right ) y''(x)-2 x y'(x)=0\) [_Gegenbauer] Solution method TO DO Maple ✓ |
| ODE 1541 |
\(n (n+1) y(x)+\left (1-x^2\right ) y''(x)-2 x y'(x)=\frac {2 ((-n-1) x P_n(x)+(n+1) P_{n+1}(x))}{x^2-1}\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1542 |
\(-p (p+1) y(x)+\left (x^2+1\right ) y''(x)+2 x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1543 |
\(p (p+1) y(x)+\left (1-x^2\right ) y''(x)-2 x y'(x)=0\) [_Gegenbauer] Solution method TO DO Maple ✓ |
| ODE 1544 |
\(n (n+2) y(x)+\left (1-x^2\right ) y''(x)-3 x y'(x)=0\) [_Gegenbauer] Solution method TO DO Maple ✓ |
| ODE 1545 |
\(-a y(x)+\left (1-x^2\right ) y''(x)-3 x y'(x)=0\) [_Gegenbauer] Solution method TO DO Maple ✓ |
| ODE 1546 |
\(\left (x^2+1\right ) y''(x)+4 x y'(x)+2 y(x)=2 (\cos (x)-x)\) [[_2nd_order, _exact, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1547 |
\(\left (x^2+1\right ) y''(x)-4 x y'(x)+6 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1548 |
\(\left (1-x^2\right ) y''(x)-\left (\left (x^2+1\right ) y(x)\right )-4 x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1549 |
\(\left (1-x^2\right ) y''(x)-6 x y'(x)-4 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1550 |
\(n y(x) (a+b+n+1)+(-x (a+b+2)-a+b) y'(x)+\left (1-x^2\right ) y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1551 |
\(p (2 k+p) y(x)-(2 k+1) x y'(x)+\left (1-x^2\right ) y''(x)=0\) [_Gegenbauer] Solution method TO DO Maple ✓ |
| ODE 1552 |
\(p (2 k+p+1) y(x)-2 (k+1) x y'(x)+\left (1-x^2\right ) y''(x)=0\) [_Gegenbauer] Solution method TO DO Maple ✓ |
| ODE 1553 |
\(-((k-p) (k+p+1) y(x))-2 (k+1) x y'(x)+\left (1-x^2\right ) y''(x)=0\) [_Gegenbauer] Solution method TO DO Maple ✓ |
| ODE 1554 |
\(-2 a x y'(x)+(1-a) a y(x)+\left (1-x^2\right ) y''(x)=0\) [_Gegenbauer] Solution method TO DO Maple ✓ |
| ODE 1555 |
\(a x y'(x)-((2-a) y(x))+\left (x^2+1\right ) y''(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1556 |
\(a x y'(x)+b y(x)+\left (1-x^2\right ) y''(x)=0\) [_Gegenbauer] Solution method TO DO Maple ✓ |
| ODE 1557 |
\(a x y'(x)+y(x) \left (\text {a0}+\text {b0} x+\text {c0} x^2\right )+\left (1-x^2\right ) y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1558 |
\((a+b x) y'(x)+c y(x)+\left (1-x^2\right ) y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1559 |
\(\left (a^2-x^2\right ) y''(x)+y(x) \left (b^2+c^2 x^2\right )-x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1560 |
\(\left (a^2-x^2\right ) y''(x)-8 x y'(x)-12 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1561 |
\((1-x) x y''(x)+2 y'(x)+y(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1562 |
\((1-x) x y''(x)-2 y'(x)+2 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1563 |
\((1-x) x y''(x)+2 y'(x)+6 y(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1564 |
\((1-x) x y''(x)-2 y'(x)+6 y(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1565 |
\((1-x) x y''(x)+3 y'(x)+2 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1566 |
\((1-x) x y''(x)-3 y'(x)+2 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1567 |
\((1-x) x y''(x)-3 y'(x)+2 y(x)=x \left (3 x^3+1\right )\) [[_2nd_order, _exact, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1568 |
\(-a y'(x)+(1-x) x y''(x)+2 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1569 |
\(x (x+1) y''(x)+(1-x) y'(x)+y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1570 |
\((1-x) x y''(x)-(x+1) y'(x)+y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1571 |
\((1-x) x y''(x)-(x+4) y'(x)+4 y(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1572 |
\((1-x) x y''(x)+2 x y'(x)-2 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1573 |
\((1-x) x y''(x)+(1-2 x) y'(x)+6 y(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1574 |
\(p (p+1) y(x)+(1-x) x y''(x)+(1-2 x) y'(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1575 |
\((1-x) x y''(x)+(1-x) y'(x)+2 y(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1576 |
\((1-x) x y''(x)-3 x y'(x)-y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1577 |
\(x (x+1) y''(x)+(3 x+2) y'(x)+y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1578 |
\((1-x) x y''(x)+(1-4 x) y'(x)-2 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1579 |
\((1-x) x y''(x)-2 (2 x+1) y'(x)-2 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1580 |
\((1-x) x y''(x)-2 (1-2 x) y'(x)-6 y(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1581 |
\((p-k) (k+p+1) y(x)+(k+1) (1-2 x) y'(x)+(1-x) x y''(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1582 |
\((c-(a+1) x) y'(x)+n (a+n) y(x)+(1-x) x y''(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1583 |
\((a+b x) y'(x)+c y(x)+x (x+1) y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1584 |
\(y'(x) (c-x (a+b+1))-a b y(x)+(1-x) x y''(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1585 |
\(-(a-(2-a) x) y'(x)-a y(x)+x (x+1) y''(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1586 |
\(-(a-(2-a) x) y'(x)-a y(x)+x (x+1) y''(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1587 |
\((a+b x) y'(x)+c y(x)+(1-x) x y''(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1588 |
\(y(x) \left (\sum _{m=0}^n a(m) x^m\right )+a (1-2 x) y'(x)+x (x+1) y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1589 |
\(\left (-x^2-x+2\right ) y''(x)+(1-x) x y'(x)+x (6 x+7) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1590 |
\((2-x) x y''(x)+2 (1-x) y'(x)+2 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1591 |
\(-\left (2-x^2\right ) y'(x)+(2-x) x y''(x)+2 (1-x) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1592 |
\((1-x)^2 y''(x)-4 (1-x) y'(x)+2 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1593 |
\((1-x)^2 y''(x)-4 (1-x) y'(x)+2 y(x)=\cos (x)\) [[_2nd_order, _exact, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1594 |
\((x+1)^2 y''(x)-4 (x+1) y'(x)+6 y(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1595 |
\((x+1)^2 y''(x)-4 (x+1) y'(x)+6 y(x)=x\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1596 |
\(-\left (-x^2-x+1\right ) y'(x)+(x+1)^2 y''(x)-(x+2) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1597 |
\((1-x)^2 y''(x)-2 (1-x)^2 y'(x)+(1-x)^2 y(x)=e^x\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1598 |
\(\left (x^2+3 x+4\right ) y''(x)+\left (x^2+x+1\right ) y'(x)-((2 x+3) y(x))=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1599 |
\((x+2)^2 y''(x)-(x+2) y'(x)+2 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1600 |
\((2-x)^2 y''(x)+(2-x) y'(x)-3 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1601 |
\(x (\text {a0}+x) y''(x)+(\text {a1}+\text {b1} x) y'(x)+\text {a2} y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1602 |
\(-4 (a+x) y'(x)+(\text {a0}+x)^2 y''(x)+6 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1603 |
\(2 x^2 y''(x)-x y'(x)+y(x)=x^2\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1604 |
\(2 x^2 y''(x)+x y'(x)-3 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1605 |
\(2 x^2 y''(x)-(2 x+7) x y'(x)+2 (x+5) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1606 |
\(2 x^2 y''(x)-(1-4 x) x y'(x)-2 (1-3 x) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1607 |
\(2 x^2 y''(x)-(1-4 x) x y'(x)-2 (1-3 x) y(x)=x^3 (x+1)\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1608 |
\(\left (2 x^2+1\right ) y''(x)+3 x y'(x)-3 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1609 |
\(2 a^2 y(x)+2 \left (1-x^2\right ) y''(x)-x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1610 |
\(2 x (x+1) y''(x)+y'(x)-4 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1611 |
\(2 (1-x) x y''(x)+(x+1) y'(x)-y(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1612 |
\(2 (1-x) x y''(x)+(1-x) y'(x)+y(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1613 |
\(2 (1-x) x y''(x)+(1-2 x) y'(x)-2 y(x)=0\) [_Jacobi, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1614 |
\(2 (1-x) x y''(x)+(1-2 x) y'(x)+8 y(x)=0\) [_Jacobi, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1615 |
\(a y(x)+2 (1-x) x y''(x)-(1-2 x) y'(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1616 |
\(y(x) (a+b x)+2 (1-x) x y''(x)+(1-2 x) y'(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1617 |
\(2 a (a+1) y(x)+2 (1-x) x y''(x)-(3 x+1) y'(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1618 |
\((1-2 x) (1-x) y''(x)+2 (1-2 x) y'(x)+4 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1619 |
\((1-2 x) (1-x) y''(x)+2 (3-4 x) y'(x)+12 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1620 |
\(2 (x+1)^2 y''(x)-(x+1) y'(x)+y(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1621 |
\(2 (x+1)^2 y''(x)-(x+1) y'(x)+y(x)=x\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1622 |
\(4 x^2 y''(x)+y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1623 |
\(4 x^2 y''(x)+y(x)=\sqrt {x}\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1624 |
\(y(x) \left (4 k x-4 p^2-x^2+1\right )+4 x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1625 |
\(\left (4 a^2 x^2+1\right ) y(x)+4 x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1626 |
\(-\left (a^2-x\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1627 |
\(4 x^2 y''(x)-\left (4 x^2+1\right ) y(x)+4 x y'(x)=4 e^x x^{3/2}\) [[_2nd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1628 |
\(-\left ((2 n+1)^2-4 x^2\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1629 |
\(-\left (a^2 x^2+1\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1630 |
\(4 x^2 y''(x)-8 x y'(x)+5 y(x)=0\) [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1631 |
\(4 x^2 y''(x)-2 (x+2) x y'(x)+(x+3) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1632 |
\(4 x^2 y''(x)-\left (-4 x^2+4 x+1\right ) y(x)+4 (1-2 x) x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1633 |
\(4 x^3 y'(x)+4 x^2 y''(x)-\left (3-2 x^2\right ) y(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1634 |
\(4 x^3 y'(x)+4 x^2 y''(x)+\left (x^4+2 x^2+1\right ) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1635 |
\(\left (a+x^4+2 x^2\right ) y(x)+4 x^3 y'(x)+4 x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1636 |
\(4 \left (1-x^2\right ) y''(x)-8 x y'(x)-y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1637 |
\(-\left (\left (4 p^2+1\right ) y(x)\right )+4 \left (1-x^2\right ) y''(x)-8 x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1638 |
\(4 \left (x^2+1\right ) y''(x)=x^2+4 x y'(x)\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1639 |
\(4 a x y'(x)-a (a+2) y(x)+4 \left (1-x^2\right ) y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1640 |
\(4 (1-x) x y''(x)+2 (1-x) y'(x)+y(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1641 |
\(y(x) (a+b x)+4 (1-x) x y''(x)+2 (1-2 x) y'(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1642 |
\(y(x) \left (a+b x+c x^2\right )+4 (1-x) x y''(x)+2 (1-2 x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1643 |
\(y(x) \left (\sum _{m=0}^n a(m) x^m\right )+4 (1-x) x y''(x)+2 (1-2 x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1644 |
\(-((k-p) (k+p+1) y(x))+2 (1-(3-2 k) x) y'(x)+4 (1-x) x y''(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1645 |
\(2 (a x+1) y'(x)+y(x) \left (b+k^2 x\right )+4 (1-x) x y''(x)=0\) [_Jacobi] Solution method TO DO Maple ✓ |
| ODE 1646 |
\((2 x+1)^2 y''(x)-2 (2 x+1) y'(x)-12 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1647 |
\((2 x+1)^2 y''(x)-2 (2 x+1) y'(x)-12 y(x)=3 x+1\) [[_2nd_order, _exact, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 1648 |
\((1-3 x)^2 y''(x)-3 (1-3 x) y'(x)-9 y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1649 |
\(16 x^2 y''(x)+(4 x+3) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1650 |
\(16 x^2 y''(x)+32 x y'(x)-(4 x+5) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1651 |
\(\left (a x^2+1\right ) y''(x)+a x y'(x)+b^2 y(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1652 |
\(\left (a x^2+1\right ) y''(x)+b x y'(x)+c y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1653 |
\(\left (1-a^2 x^2\right ) y''(x)-2 a^2 x y'(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1654 |
\(\left (1-a^2 x^2\right ) y''(x)-2 a^2 x y'(x)+2 a^2 y(x)=0\) [_Gegenbauer] Solution method TO DO Maple ✓ |
| ODE 1655 |
\(x (a+b x) y''(x)+2 a y'(x)-2 b y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1656 |
\(y''(x) \left (\text {a0}+\text {b0} x+\text {c0} x^2\right )+(\text {a1}+\text {b1} x) y'(x)+2 \text {a2} y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1657 |
\(\text {a1} (a+b x) y'(x)+(a+b x)^2 y''(x)+\text {a2} y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1658 |
\(x^3 y''(x)=a+b x\) [[_2nd_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 1659 |
\(x^3 y''(x)+x y'(x)-y(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1660 |
\(x^3 y''(x)+x y'(x)-2 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1661 |
\(x^3 y''(x)+2 x y'(x)-y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1662 |
\(\text {a1} x y'(x)+y(x) (\text {a2}+\text {b2} x)+x^3 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1663 |
\(y(x) \left (a+b x+c x^2\right )+x^3 y''(x)+x^2 y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1664 |
\(x^3 y''(x)+3 x^2 y'(x)+x y(x)=0\) [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1665 |
\(x^3 y''(x)+3 x^2 y'(x)+x y(x)=1\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1666 |
\(a x^2 y'(x)+y(x) (b+c x)+x^3 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1667 |
\(\left (\text {a1}+\text {b1} x^2\right ) y'(x)+\text {a2} x y(x)+x^3 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1668 |
\(x (\text {a1}+\text {b1} x) y'(x)+\text {a2} y(x)+x^3 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1669 |
\(x (\text {a1}+\text {b1} x) y'(x)+y(x) (\text {a2}+\text {b2} x)+x^3 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1670 |
\(\left (1-x^3\right ) y''(x)+6 x y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1671 |
\(x \left (1-x^2\right ) y''(x)-y'(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1672 |
\(x^3+\left (1-x^2\right ) x y''(x)-y'(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1673 |
\(a x^3 y(x)+\left (1-x^2\right ) x y''(x)-y'(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1674 |
\(x \left (1-x^2\right ) y''(x)-\left (x^2+7\right ) y'(x)+4 x y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1675 |
\(x \left (x^2+1\right ) y''(x)-2 \left (x^2+1\right ) y'(x)+2 x y(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1676 |
\(x \left (x^2+1\right ) y''(x)-2 \left (1-x^2\right ) y'(x)-2 x y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1677 |
\(x \left (1-x^2\right ) y''(x)-2 \left (1-x^2\right ) y'(x)-2 x y(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1678 |
\(\left (a+b x^2\right ) y'(x)+c x y(x)+x \left (x^2+1\right ) y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1679 |
\(\left (a+b x^2\right ) y'(x)+(a-1) x (a+b) y(x)+x \left (1-x^2\right ) y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1680 |
\(\left (a+b x^2\right ) y'(x)+2 (1-b) x y(x)+x \left (1-x^2\right ) y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1681 |
\(\left (a-(a+1) x^2\right ) y'(x)+c x y(x)+x \left (1-x^2\right ) y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1682 |
\(\left (a+b x^2\right ) y'(x)+c x y(x)+x \left (1-x^2\right ) y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1683 |
\(x \left (x^2+2\right ) y''(x)-y'(x)-6 x y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1684 |
\(x \left (2-x^2\right ) y''(x)-\left (\left (x^2+4 x+2\right ) y(x)\right )-\left (-x^3-3 x^2+2 x+2\right ) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1685 |
\(x \left (\text {a0}+x^2\right ) y''(x)+\left (\text {a1}+\text {b1} x^2\right ) y'(x)+\text {a2} x y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1686 |
\(x^2 (x+1) y''(x)+x y'(x)+(x+1)^3 (-y(x))=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1687 |
\((1-x) x^2 y''(x)-(x+1) x y'(x)+y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1688 |
\((x+1) x^2 y''(x)-(2 x+1) x y'(x)+(2 x+1) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1689 |
\((1-x) x^2 y''(x)+2 (2-x) x y'(x)+2 (x+1) y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1690 |
\((1-x) x^2 y''(x)-(4-5 x) x y'(x)+(6-9 x) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1691 |
\((x+1) x^2 y''(x)+2 (3 x+2) x y'(x)+2 (3 x+1) y(x)=0\) [[_2nd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 1692 |
\(x (\text {a1}+\text {b1} x) y'(x)+y(x) (\text {a2}+\text {b2} x)+(1-x) x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1693 |
\(x^2 (\text {a0}+x) y''(x)+x (\text {a1}+\text {b1} x) y'(x)+y(x) (\text {a2}+\text {b2} x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1694 |
\((1-x)^2 x y''(x)-2 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1695 |
\(x \left (x^2+1\right ) y''(x)+x (x+1) y'(x)+y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1696 |
\(x (2-x)^2 y''(x)+2 (2-x) y'(x)+2 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1697 |
\((1-x) x (a-x) y''(x)+y'(x) \left (x^2 (\text {a0}+\text {a1}+1)+\text {a0} \text {a2}-\text {a0}+\text {a1}+x (\text {a2}+\text {a3})-\text {a3}+1\right )+\text {a0} \text {a1} (x-k) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1698 |
\((\text {a1}-x) (\text {a2}-x) (\text {a3}-x) y''(x)+y'(x) \left (\text {b0}+\text {b1} x+\text {b2} x^2\right )+y(x) (\text {c0}+\text {c1} x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1699 |
\(\left (1-2 x^3\right ) y''(x)+6 x^2 y'(x)-6 x y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1700 |
\(2 (1-x) x^2 y''(x)+(3-5 x) x y'(x)-(x+1) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1701 |
\(2 (2-x) x^2 y''(x)-(4-x) x y'(x)+(3-x) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1702 |
\(x \left (3 x^2+1\right ) y''(x)+2 y'(x)-6 x y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1703 |
\(4 (x+1) x^2 y''(x)-4 x^2 y'(x)+(3 x+1) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1704 |
\(x^2 (a+b x) y''(x)-2 x (2 a+b x) y'(x)+2 y(x) (3 a+b x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1705 |
\(y(x) (a+b x)+4 (1-x) x y''(x)+2 (1-3 x) (1-x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1706 |
\(4 (1-x) x (1-a x) y''(x)+y'(x) \left (\text {a0}+\text {a1} x+\text {a2} x^2\right )+y(x) \left (\text {b0}+\text {b1} x^2\right )=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1707 |
\(a^2 y(x)+x^4 y''(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1708 |
\(x^4 y''(x)+\left (1-2 x^2\right ) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1709 |
\(x^4 y''(x)-\left (2 x^2+1\right ) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1710 |
\(\left (e^{2/x}-a^2\right ) y(x)+x^4 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1711 |
\(x^4 y''(x)+x y'(x)-2 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1712 |
\(x^4 y''(x)-2 x^2 y'(x)+(2 x+1) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1713 |
\(x^4 y''(x)+x^3 y'(x)+y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1714 |
\(x^4 y''(x)+x^3 y'(x)-(x+1) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1715 |
\(y(x) \left (a+b x^2+c x^4\right )+x^4 y''(x)+x^3 y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1716 |
\(x^4 y''(x)+\left (x^2+1\right ) x y'(x)+y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1717 |
\(x^4 y''(x)-\left (1-x^2\right ) x y'(x)+\left (1-x^2\right ) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1718 |
\(a^2 y(x)+x^4 y''(x)+2 x^3 y'(x)=0\) [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1719 |
\(x^4 y''(x)+\left (2 x^2+1\right ) x y'(x)-y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1720 |
\(2 x^2 (a+x) y'(x)+b y(x)+x^4 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1721 |
\(\left (x^3+1\right ) x y''(x)-\left (1-x^3\right ) y'(x)+x^2 (-y(x))=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1722 |
\(x^3 \left (-y'(x)\right )+\left (1-x^2\right ) x^2 y''(x)-2 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1723 |
\(\left (1-x^2\right ) x^2 y''(x)-\left (2-x^2\right ) x y'(x)+\left (2-x^2\right ) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1724 |
\(a (a+1) y(x)-2 x^3 y'(x)+\left (1-x^2\right ) x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1725 |
\(\left (x^2+1\right )^2 y''(x)+2 x \left (x^2+1\right ) y'(x)+y(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1726 |
\(\left (x^2+1\right )^2 y''(x)+2 x \left (x^2+1\right ) y'(x)+4 y(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1727 |
\(a^2 (-y(x))+\left (x^2+1\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1728 |
\(-y(x) \left (m^2-n (n+1) \left (1-x^2\right )\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1729 |
\(-y(x) \left (k^2-p (p+1) \left (1-x^2\right )\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1730 |
\(-y(x) \left (a^2-k \left (1-x^2\right )\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1731 |
\(y(x) \left (\text {a0}+\text {a2} x^2+\text {a4} x^4\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1732 |
\(y(x) \left (\sum _{m=0}^n a(m) x^m\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1733 |
\(a x \left (1-x^2\right ) y'(x)+b y(x)+\left (x^2+1\right )^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1734 |
\(\text {a1} x \left (1-x^2\right ) y'(x)+y(x) \left (\text {a2}+\text {b2} x+\text {c2} x^2\right )+\left (1-x^2\right )^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1735 |
\(x^2 \left (a^2+x^2\right )^2 y''(x)+x \left (a^2+2 x^2\right ) y'(x)+b^2 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1736 |
\(\left (a^2+x^2\right )^2 y''(x)+2 x \left (a^2+2 x^2\right ) y'(x)-y(x) \left (\text {a0}+\text {a2} x^2+\text {a4} x^4\right )=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1737 |
\(\left (a^2-x^2\right )^2 y''(x)-2 x \left (a^2-x^2\right ) y'(x)+y(x) \left (\text {a0}+\text {a2} x^2+\text {a4} x^4\right )=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1738 |
\(\left (a^2+x^2\right )^2 \left (b^2+x^2\right ) y''(x)+x \left (\text {a0}+\text {b0} x^2\right ) y'(x)+y(x) \left (\text {a1}+\text {b1} x^2\right )=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1739 |
\(\left (a^2-x^2\right )^2 \left (b^2-x^2\right ) y''(x)+x \left (\text {a0}+\text {b0} x^2\right ) y'(x)+y(x) \left (\text {a1}+\text {b1} x^2+\text {c1} x^4\right )=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1740 |
\((1-x) x (x+1)^2 y''(x)+2 (3-x) x (x+1) y'(x)-2 (1-x) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1741 |
\(y(x) \left (a+b x+c x^2\right )+(1-x)^2 x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1742 |
\((1-x)^2 x^2 y''(x)+(1-2 x) (1-x) x y'(x)-y(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1743 |
\((1-x) x (\text {a1}+\text {b2} x) y'(x)+y(x) \left (\text {a2}+\text {b2} x+\text {c2} x^2\right )+(1-x)^2 x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1744 |
\(y(x) \left (\sum _{m=0}^n a(m) x^m\right )+(1-x)^2 x^2 y''(x)+(1-2 x) (1-x) x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1745 |
\(x^2 (a-x)^2 y''(x)+b y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1746 |
\((a-x)^2 (b-x)^2 y''(x)=k^2 y(x)\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1747 |
\((a-x) (A+2 x) (b-x) y'(x)+(a-x)^2 (b-x)^2 y''(x)+B y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1748 |
\((a-x)^4 y''(x)-2 (a-x)^3 y'(x)-y(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1749 |
\((1-2 x) (1-x) x^2 y''(x)+2 (2-3 x) x y'(x)+2 (3 x+1) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1750 |
\((1-2 x) (1-x) x^2 y''(x)+2 (1-2 x) (2-x) x y'(x)+2 (1-x) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1751 |
\(-y(x) \left (4 k^2+\left (4 p^2+1\right ) \left (1-x^2\right )\right )+4 \left (1-x^2\right )^2 y''(x)-8 x \left (1-x^2\right ) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1752 |
\(-y(x) \left (4 k^2+\left (1-4 p^2\right ) \left (1-x^2\right )\right )+4 \left (1-x^2\right )^2 y''(x)-8 x \left (1-x^2\right ) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1753 |
\(-y(x) \left (a (a+1) (1-x)+b^2 x\right )+4 \left (1-x^2\right ) x^2 y''(x)+2 (1-3 x) (1-x) x y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1754 |
\((a+b x)^4 y''(x)+y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1755 |
\(y''(x) \left (a+b x+c x^2\right )^2+A y(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1756 |
\(x^5 y''(x)+x y'(x)-y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1757 |
\(x^5 y''(x)-\left (1-2 x^3\right ) x y'(x)+\left (1-2 x^3\right ) y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1758 |
\(x \left (a^2-x^2\right ) \left (b^2-x^2\right ) y''(x)+\left (\text {a0}+\text {b0} x^4\right ) y'(x)+x^3 y(x) \left (\text {a1}+\text {b1} x^2+\text {c1} x^4\right )=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1759 |
\(a y(x)+x^6 y''(x)-x^5 y'(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1760 |
\(x^6 y''(x)+3 x^5 y'(x)+y(x)=0\) [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1761 |
\(x^3 \left (a+3 x^2\right ) y'(x)+x^6 y''(x)+y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1762 |
\((a-x) (b-x) (c-x) y'(x) \left (\text {a1}+\text {b1} x+\text {c1} x^2\right )+(a-x)^2 (b-x)^2 (c-x)^2 y''(x)+y(x) \left (\text {a2}+\text {b2} x+\text {c2} x^2\right )=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1763 |
\(4 x^6 y''(x)+\left (1-2 x^2\right ) y(x)+4 \left (2 x^2+1\right ) x^3 y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1764 |
\(4 x^6 y''(x)+\left (8 x^4+10 x^2+1\right ) y(x)-4 \left (2 x^2+1\right ) x^3 y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1765 |
\(\left (4 b-a^2\right ) y(x)+4 x^6 y''(x)+12 x^5 y'(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1766 |
\(x^{2 a} y''(x)+a x^{2 a-1} y'(x)+(1-a)^2 y(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]] Solution method TO DO Maple ✓ |
| ODE 1767 |
\(a^2 x^{a-1} y(x)+x^{a+1} y''(x)+(1-2 a) x^a y'(x)=0\) [[_Emden, _Fowler]] Solution method TO DO Maple ✓ |
| ODE 1768 |
\(x^2 y''(x) \left (\text {a0}+\text {b0} x^k\right )+x y'(x) \left (\text {a1}+\text {b1} x^k\right )+y(x) \left (\text {a2}+\text {b2} x^k\right )=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1769 |
\(\left (1-a^2 \cos ^2(x)\right ) y''(x)+a^2 \sin (x) \cos (x) y'(x)+y(x) \left (\text {a0}+\text {a1} \cos ^2(x)\right )=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1770 |
\(-y(x) \left (4 k^2-\left (1-p^2\right ) \sinh ^2(x)\right )+4 \sinh ^2(x) y''(x)+4 \sinh (x) \cosh (x) y'(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1771 |
\(y''(x)=0\) [[_2nd_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 1772 |
\(y''(x)=a y(x)\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1773 |
\(y''(x)=6 y(x)^2\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1774 |
\(y''(x)=6 y(x)^2+x\) [[_Painleve, `1st`]] Solution method TO DO Maple ✗ |
| ODE 1775 |
\(y''(x)=a+b x+c y(x)^2\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1776 |
\(y''(x)=2 y(x)^3\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1777 |
\(y''(x)=a+b y(x)+2 y(x)^3\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1778 |
\(y''(x)=a+2 y(x)^3+x y(x)\) [[_Painleve, `2nd`]] Solution method TO DO Maple ✗ |
| ODE 1779 |
\(y''(x)=f(x)+g(x) y(x)+2 y(x)^3\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1780 |
\(y''(x)=-2 a b x y(x)+a+2 b^2 y(x)^3\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1781 |
\(y''(x)=\text {a0}+\text {a1} x y(x)+\text {a2} y(x)+\text {a3} y(x)^3\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1782 |
\(y''(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2+\text {a3} y(x)^3\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1783 |
\(a x^r y(x)^s+y''(x)=0\) [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1784 |
\(a \sin (y(x))+y''(x)=0\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1785 |
\(a e^{y(x)}+y''(x)=0\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1786 |
\(y''(x)=f(y(x))\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1787 |
\(y(x) \left (f'(x)+2 f(x)^2\right )+3 f(x) y'(x)+y''(x)=2 y(x)^3\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 1788 |
\(y''(x)+y(x) y'(x)=0\) [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1789 |
\(y''(x)+y(x) y'(x)=y(x)^3\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1790 |
\(a y(x)+y''(x)+y(x) y'(x)=y(x)^3\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1791 |
\(y''(x)+y(x) y'(x)=12 f'(x)-12 f(x) y(x)+y(x)^3\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 1792 |
\(2 a^2 y(x)+(3 a+y(x)) y'(x)+a y(x)^2+y''(x)=y(x)^3\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1793 |
\(y''(x)=y(x) \left (f'(x)-2 f(x)^2\right )+(3 f(x)-y(x)) y'(x)+f(x) y(x)^2+y(x)^3\) odeadvisor timed out Solution method TO DO Maple ✓ |
| ODE 1794 |
\(y''(x)=(3 \text {f1}(x)-y(x)) y'(x)+\text {f1}(x) y(x)^2+\text {f2}(x)+\text {f3}(x) y(x)+y(x)^3\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1795 |
\(y''(x)=y'(x) (\text {f0}(x) y(x)+\text {f1}(x))+\text {g0}(x) y(x)^3+\text {g1}(x) y(x)^2+\text {g2}(x) y(x)+\text {g3}(x)\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1796 |
\(y''(x)=y(x) f'(x)+(f(x)-2 y(x)) y'(x)\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 1797 |
\(y''(x)=(f(x)-2 y(x)) y'(x)+f(x) y(x)^2+g(x)\) [[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✗ |
| ODE 1798 |
\(y''(x)=(\text {f1}(x)-2 y(x)) y'(x)+\text {f2}(x) y(x)^2+\text {f3}(x)\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1799 |
\(y''(x)=(\text {f1}(x)-2 y(x)) y'(x)+\text {f2}(x) y(x)^2+\text {f3}(x) y(x)+\text {f4}(x)\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1800 |
\(y''(x)=a+4 b^2 y(x)+3 b y(x)^2+3 y(x) y'(x)\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1801 |
\(y''(x)+3 y(x) y'(x)=f(x)+g(x) y(x)-y(x)^3\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1802 |
\(y''(x)=(f(x)-3 y(x)) y'(x)+f(x) y(x)^2-y(x)^3\) [[_2nd_order, _with_potential_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1803 |
\(y''(x)=a \left (2 y(x) y'(x)+1\right )\) [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1804 |
\(a \left (y(x)^2-1\right ) y'(x)+b y(x)+y''(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✗ |
| ODE 1805 |
\(y'(x) f(x,y(x))+g(x,y(x))+y''(x)=0\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1806 |
\(y''(x)=\left (x^2-y'(x)\right )^2+2 x\) [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1807 |
\(y''(x)+2 y'(x)^2 \tan (y(x))+2 \cot (x) y'(x)=0\) [_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1808 |
\(y''(x)=a y'(x)^2\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1809 |
\(y''(x)=a^2+b^2 y'(x)^2\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1810 |
\(a y'(x)^2+b y(x)+y''(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1811 |
\(a y'(x)^2+b \sin (y(x))+y''(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1812 |
\(a y'(x)^2+b y'(x)+c y(x)+y''(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✗ |
| ODE 1813 |
\(y''(x)=e^x y'(x)^2\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1814 |
\(f(x) y'(x)+g(x) y'(x)^2+y''(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1815 |
\(a y(x) y'(x)^2+b y(x)+y''(x)=0\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1816 |
\(f(y(x)) y'(x)^2+g(y(x))+y''(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1817 |
\(f(x) y'(x)+g(y(x)) y'(x)^2+y''(x)=0\) [_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1818 |
\(f(y(x)) y'(x)+g(y(x)) y'(x)^2+y''(x)=0\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1819 |
\(f(y(x)) y'(x)+g(y(x)) y'(x)^2+h(y(x))+y''(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✗ |
| ODE 1820 |
\(y''(x)+y'(x)^3+y'(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1821 |
\(y''(x)=(a-x) y'(x)^3\) [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1822 |
\(y''(x)+\left (e^{2 y(x)}+x\right ) y'(x)^3=0\) [[_2nd_order, _with_exponential_symmetries], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1823 |
\(y''(x)+4 y'(x)^3+2 y'(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1824 |
\(a y'(x)^3+y''(x)=0\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1825 |
\(y''(x)=x y'(x)^3\) [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1826 |
\(y'(x)^3 (a x+b y(x))+y''(x)=0\) [[_2nd_order, _with_exponential_symmetries], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1827 |
\(a y(x) \left (y'(x)^2+1\right )^2+y''(x)=0\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1828 |
\(y''(x)=a \left (x y'(x)-y(x)\right )^k\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1829 |
\(f(x) y'(x)^k+g(x) y'(x)+y''(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1830 |
\(y''(x)=A x^a y(x)^b y'(x)^c\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1831 |
\(y''(x)=a \sqrt {y'(x)^2+1}\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1832 |
\(y''(x)=a \sqrt {b y(x)^2+y'(x)^2}\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1833 |
\(y''(x)=a \left (y'(x)^2+1\right )^{3/2}\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1834 |
\(y''(x)=a x \left (y'(x)^2+1\right )^{3/2}\) [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1835 |
\(y''(x)=a y(x) \left (y'(x)^2+1\right )^{3/2}\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1836 |
\(y''(x)=a y(x) \left (\left (b-y'(x)\right )^2+1\right )^{3/2}\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1837 |
\(y''(x)=a \left (y'(x)^2+1\right )^{3/2} (b+c x+y(x))\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1838 |
\(y''(x)+y(x)^3 y'(x)=y(x) y'(x) \sqrt {4 y'(x)+y(x)^4}\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1839 |
\(y''(x)=f\left (y'(x)\right )\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1840 |
\(y''(x)=f\left (a x+b y(x),y'(x)\right )\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1841 |
\(y''(x)=y(x) f\left (x,\frac {y'(x)}{y(x)}\right )\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1842 |
\(y''(x)=x^{n-2} f\left (x^{-n} y(x),x^{1-n} y'(x)\right )\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1843 |
\(2 y''(x)=12 y(x)^2+1\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1844 |
\(2 y''(x)=y(x) \left (a-y(x)^2\right )\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1845 |
\(8 y''(x)+9 y'(x)^4=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1846 |
\(a x e^{y(x)}+x y''(x)+y'(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1847 |
\(x y''(x)+2 y'(x)+x y(x)^5=0\) [_Emden, [_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1848 |
\(x y(x)^n+x y''(x)+2 y'(x)=0\) [_Emden, [_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1849 |
\(x^m y(x)^n+x y''(x)+2 y'(x)=0\) [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1850 |
\(a x^m y(x)^n+x y''(x)+2 y'(x)=0\) [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1851 |
\(a y'(x)+b x e^{y(x)}+x y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1852 |
\(\left (2-a x^2\right ) y'(x)+x y''(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1853 |
\(x y''(x)=(1-y(x)) y'(x)\) [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1854 |
\(x y''(x)+x y'(x)^2=y'(x)\) [[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1855 |
\(x y''(x)=x y'(x)^2+y'(x)\) [[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1856 |
\(x y''(x)+2 x y'(x)^2-2 y'(x)=0\) [[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1857 |
\(x y''(x)=x^2 y'(x)^2-2 y'(x)-y(x)^2\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1858 |
\(a x^2 y'(x)^2+x y''(x)+2 y'(x)=b\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1859 |
\(\left (a x y'(x)-y(x)\right )^2+x y''(x)=b\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1860 |
\(x y''(x)=y'(x)^3+y'(x)\) [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1861 |
\(x y''(x)+2 y'(x)=a x^{2 k} y'(x)^k\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1862 |
\(2 x y''(x)+y'(x)^3+y'(x)=0\) [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1863 |
\(a y(x) \left (1-y(x)^n\right )+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1864 |
\(a e^{y(x)-1}+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1865 |
\((a+1) x y'(x)+x^2 y''(x)=x^k f\left (x^k y(x),k y(x)+x y'(x)\right )\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1866 |
\(x^2 y''(x)+y'(x)^2=0\) [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1867 |
\(x^2 y''(x)=\left (3 x-2 y'(x)\right ) y'(x)\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1868 |
\(x^2 y''(x)+x^2 y'(x)^2+4 x y'(x)+2=0\) [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1869 |
\(x^2 y''(x)=x^4 y'(x)^2-4 x^2 y(x)^2+6 y(x)\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1870 |
\(a \left (x y'(x)-y(x)\right )^2+x^2 y''(x)=b x^2\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1871 |
\(a x^4 y'(x)^2+x^2 y''(x)+2 x y(x)=b\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1872 |
\(a y(x) y'(x)^2+b x+x^2 y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1873 |
\(x^2 y''(x)=\sqrt {a x^2 y'(x)^2+b y(x)^2}\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1874 |
\(x^2 y''(x)=y(x) f\left (\frac {x y'(x)}{y(x)}\right )\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1875 |
\(\left (x^2+1\right ) y''(x)+y'(x)^2+1=0\) [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1876 |
\(a y(x)^3+9 x^2 y''(x)+2 y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1877 |
\(x^3 y''(x)-x^2 y'(x)=3-x^2\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 1878 |
\(x^3 \left (y''(x)+y(x) y'(x)-y(x)^3\right )+12 x y(x)+24=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1879 |
\(x^3 y''(x)=a \left (x y'(x)-y(x)\right )^2\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1880 |
\(2 x^3 y''(x)+x^2 (2 x y(x)+9) y'(x)+x y(x) \left (-2 x^2 y(x)^2+3 x y(x)+12\right )-6=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1881 |
\(x^4 y''(x)=x \left (x^2+2 y(x)\right ) y'(x)-4 y(x)^2\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1882 |
\(x^4 y''(x)=x^2 y'(x) \left (y'(x)+x\right )-4 y(x)^2\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1883 |
\(x^4 y''(x)+\left (x y'(x)-y(x)\right )^3=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1884 |
\(x^a y''(x)+y(x)^b=0\) [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1885 |
\(\left (1-12 x^2\right ) \left (3 y'(x)+y(x)^2\right )+2 x \left (1-4 x^2\right ) \left (y''(x)+y(x) y'(x)-y(x)^3\right )-48 x y(x)+24=0\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1886 |
\(a x y(x)+b-\left (k x^{k-1}-12 x^2\right ) \left (3 y'(x)+y(x)^2\right )+2 \left (x^k-4 x^3\right ) \left (y''(x)+y(x) y'(x)-y(x)^3\right )=0\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1887 |
\(\sqrt {x} y''(x)=y(x)^{3/2}\) [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1888 |
\(x^{3/2} y''(x)=f\left (\frac {y(x)}{\sqrt {x}}\right )\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 1889 |
\(y''(x) \left (a+2 b x+c x^2\right )^{3/2}=f\left (\frac {x}{\sqrt {a+2 b x+c x^2}}\right )\) [[_2nd_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 1890 |
\(f(x) f'(x) y'(x)+f(x)^2 y''(x)=g\left (y(x),f(x) y'(x)\right )\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 1891 |
\(f(x)^2 y''(x)=y'(x) \left (3 f(x) f'(x)-f(x)^2 y(x)+3 f(x)^3\right )-24 f(x)^4\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 1892 |
\(f(x)^2 y''(x)=-a f(x)^5+3 f(x) f'(x)-f(x)^2 y(x)+3 f(x)^3\) odeadvisor timed out Solution method TO DO Maple ✓ |
| ODE 1893 |
\(2 f(x)^2 y''(x)=f(x) y'(x) \left (3 f'(x)-2 f(x) y(x)\right )+f(x) y(x)^2 f'(x)+y(x) \left (f(x) f''(x)-2 f'(x)^2-2 f(x)^3\right )+2 f(x)^2 y(x)^3\) odeadvisor timed out Solution method TO DO Maple ✓ |
| ODE 1894 |
\(y(x) y''(x)=a\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1895 |
\(y(x) y''(x)=y'(x)^2\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1896 |
\(y(x) y''(x)+y'(x)^2=0\) [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1897 |
\(y(x) y''(x)=y'(x)^2-a^2\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1898 |
\(y(x) y''(x)+y'(x)^2=a^2\) [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1899 |
\(y(x) y''(x)+y'(x)^2+y(x)^2=0\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1900 |
\(2 a^2 y(x)^2+y(x) y''(x)+y'(x)^2=0\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1901 |
\(y(x) y''(x)=\text {a0}+\text {a1} y(x)+y(x)^3 (\text {a2}+\text {a3} y(x))+y'(x)^2\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1902 |
\(y(x) y''(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2+\text {a3} y(x)^3+\text {a4} y(x)^4+y'(x)^2\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1903 |
\(y(x) y''(x)=y'(x)^2+y(x) y'(x)\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1904 |
\(y(x) y''(x)=e^x y(x) \left (\text {a0}+\text {a1} y(x)^2\right )+e^{2 x} \left (\text {a2}+\text {a3} y(x)^4\right )+y'(x)^2\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1905 |
\(y(x) y''(x)=y'(x)^2+y(x)^2 \log (y(x))\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1906 |
\(y(x) y''(x)=-x^2 y(x)^2+y'(x)^2+y(x)^2 \log (y(x))\) [[_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1907 |
\(y(x) y''(x)+y'(x)^2=y'(x)\) [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1908 |
\(y(x) y''(x)=y'(x)^2-y'(x)\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1909 |
\(y(x) y''(x)=y(x)^2 \left (f(x) y(x)+g'(x)\right )+y'(x)^2+y'(x)\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 1910 |
\(y(x) y''(x)=y'(x)^2-2 y'(x)\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1911 |
\(y(x) y''(x)+y'(x)^2-x y'(x)+y(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1912 |
\(a x y'(x)+y(x) y''(x)+y'(x)^2=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1913 |
\(y(x) y''(x)=-y(x) f'(x)+f(x) y'(x)+y'(x)^2+y(x)^3\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 1914 |
\(y(x) y''(x)=y(x) f''(x)-f(x) y'(x)-f(x) y(x)^3+y'(x)^2+y(x)^4\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 1915 |
\(y(x) y''(x)=-a y(x) y'(x)-b y(x)^2+y'(x)^2\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1916 |
\(y(x) y''(x)=a y(x) y'(x)+b y(x)^2+y'(x)^2+y(x)^3\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✗ |
| ODE 1917 |
\(y(x) y''(x)=y(x)^2 y'(x)+y'(x)^2\) [[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1918 |
\(y(x) y''(x)=f(x) y(x) y'(x)+g(x) y(x)^2+y'(x)^2\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1919 |
\(y(x) y''(x)=-y(x) \left (f'(x)-y(x)^2 g'(x)\right )+y'(x) \left (f(x)+g(x) y(x)^2\right )+y'(x)^2\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 1920 |
\(y(x) y''(x)=2 y'(x)^2+y(x)^2\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1921 |
\(y(x) y''(x)=2 \left (y'(x)^2-y(x)^2\right )\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1922 |
\(y(x) y''(x)=-3 y(x) y'(x)+3 y'(x)^2+y(x)^2\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1923 |
\(y(x) y''(x)=a y'(x)^2\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1924 |
\(y(x) y''(x)=a y'(x)^2+b\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1925 |
\(y(x) y''(x)=a y'(x)^2+b y(x)^3\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1926 |
\(y(x) y''(x)=a y'(x)^2+\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2+\text {a3} y(x)^3+\text {a3} y(x)^2+\text {a4} y(x)^4\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1927 |
\(y(x) y''(x)=a y'(x)^2+b y(x) y'(x)+c y(x)^2\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1928 |
\(y(x) y''(x)=\text {a3} y(x)^{a+1}+a y'(x)^2+\text {a1} y(x) y'(x)+\text {a2} y(x)^2\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1929 |
\(a y'(x)^2+f(x) y(x) y'(x)+g(x) y(x)^2+y(x) y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1930 |
\(y(x) y''(x)+y'(x)^3=0\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1931 |
\(y(x) y''(x)+y'(x)^3-y'(x)^2=0\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1932 |
\(y(x) y''(x)=y'(x)^2 \left (y'(x) (-\sin (y(x)))-y(x) y'(x) \cos (y(x))+1\right )\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1933 |
\((1-y(x)) y''(x)+2 y'(x)^2=0\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1934 |
\((a+y(x)) y''(x)=y'(x)^2\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1935 |
\((a+y(x)) y''(x)+y'(x)^2=b\) [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1936 |
\((a+y(x)) y''(x)+b y'(x)^2=0\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1937 |
\((y(x)+x) y''(x)+y'(x)^2-y'(x)=0\) [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1938 |
\((x-y(x)) y''(x)+2 y'(x) \left (y'(x)+1\right )=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1939 |
\((x-y(x)) y''(x)=\left (y'(x)+1\right ) \left (y'(x)^2+1\right )\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1940 |
\((x-y(x)) y''(x)=f\left (y'(x)\right )\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 1941 |
\(2 y(x) y''(x)=y'(x)^2\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1942 |
\(2 y(x) y''(x)+y'(x)^2+1=0\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1943 |
\(2 y(x) y''(x)=a+y'(x)^2\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1944 |
\(2 y(x) y''(x)=y'(x)^2+8 y(x)^3\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1945 |
\(2 y(x) y''(x)=y'(x)^2+8 y(x)^3+4 y(x)^2\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1946 |
\(2 y(x) y''(x)=y'(x)^2+4 (2 y(x)+x) y(x)^2\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1947 |
\(2 y(x) y''(x)=y(x)^2 (a+b y(x))+y'(x)^2\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1948 |
\(2 y(x) y''(x)=a y(x)^3+y'(x)^2-2 x y(x)^2-1\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1949 |
\(2 y(x) y''(x)=y(x)^2 (a x+b y(x))+y'(x)^2\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1950 |
\(2 y(x) y''(x)=y'(x)^2+3 y(x)^4\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1951 |
\(2 y(x) y''(x)=-a^2-4 \left (b-x^2\right ) y(x)^2+y'(x)^2+3 y(x)^4+8 x y(x)^3\) [[_Painleve, `4th`]] Solution method TO DO Maple ✗ |
| ODE 1952 |
\(2 y(x) y''(x)=-2 y(x)^2 \left (f'(x)+f(x)^2\right )-3 f(x) y(x) y'(x)+y'(x)^2+8 y(x)^3\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 1953 |
\(2 y(x) y''(x)=2 x f(x) y(x)^2-4 y(x)^2 y'(x)+y'(x)^2-y(x)^4-1\) [NONE] Solution method TO DO Maple ✗ |
| ODE 1954 |
\(2 y(x) y''(x)=3 y'(x)^2\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1955 |
\(2 y(x) y''(x)=3 y'(x)^2+4 y(x)^2\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1956 |
\(2 y(x) y''(x)=f(x) y(x)^2+3 y'(x)^2\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1957 |
\(2 y(x) y''(x)=6 y'(x)^2+\left (1-3 y(x)^2\right ) y(x)^2\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1958 |
\(2 y(x) y''(x)=6 y'(x)^2-y(x)^2 \left (a y(x)^3+1\right )\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1959 |
\(2 y(x) y''(x)=y'(x)^2 \left (y'(x)^2+1\right )\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 1960 |
\(3 y(x) y''(x)=2 y'(x)^2+36 y(x)^2\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1961 |
\(3 y(x) y''(x)=5 y'(x)^2\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1962 |
\(4 y(x) y''(x)=3 y'(x)^2-4 y(x)\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1963 |
\(4 y(x) y''(x)=3 y'(x)^2+12 y(x)^2\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1964 |
\(4 y(x) y''(x)=a y(x)+b y(x)^2+c y(x)^3+3 y'(x)^2\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1965 |
\(5 y(x) y''(x)=y'(x)^2\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1966 |
\(12 y(x) y''(x)=15 y'(x)^2-8 y(x)^3\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 1967 |
\(a y(x) y''(x)=(a-1) y'(x)^2\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1968 |
\(a (a+2)^2 y(x) y''(x)=a^2 (a+2) y(x)^3 f'(x)-a^2 f(x)^2 y(x)^4+a (a+2)^2 f(x) y(x)^2 y'(x)+(a-1) (a+2)^2 y'(x)^2\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 1969 |
\(x y(x) y''(x)+x y'(x)^2+y(x) y'(x)=0\) [[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1970 |
\(x y(x) y''(x)+x y'(x)^2=y(x) y'(x)\) [[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1971 |
\(x y(x) y''(x)=x y'(x)^2-y(x) y'(x)\) [_Liouville, [_Painleve, `3rd`], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1972 |
\(x y(x) y''(x)=x \left (\text {a0}+\text {a1} y(x)^4\right )+y(x) \left (\text {a2}+\text {a3} y(x)^2\right )+x y'(x)^2-y(x) y'(x)\) [[_Painleve, `3rd`]] Solution method TO DO Maple ✗ |
| ODE 1973 |
\(x y(x) y''(x)+x y'(x)^2+2 y(x) y'(x)=0\) [[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1974 |
\(x y(x) y''(x)+x y'(x)^2=3 y(x) y'(x)\) [[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1975 |
\(a y(x) y'(x)+f(x)+x y(x) y''(x)+x y'(x)^2=0\) [[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1976 |
\(x y(x) y''(x)=a y(x) y'(x)+x y'(x)^2+x y(x)^3\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1977 |
\(x y(x) y''(x)=a y(x) y'(x)+b^2 x y(x)^3+x y'(x)^2\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 1978 |
\(x y(x) y''(x)+2 x y'(x)^2+y(x) y'(x)=0\) [_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1979 |
\(x y(x) y''(x)-2 x y'(x)^2+y(x) y'(x)=0\) [_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1980 |
\(x y(x) y''(x)-2 x y'(x)^2-y(x) y'(x)=0\) [_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1981 |
\(x y(x) y''(x)=2 x y'(x)^2-(y(x)+1) y'(x)\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1982 |
\(a y(x) y'(x)+x y(x) y''(x)+2 x y'(x)^2=0\) [_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1983 |
\(a y(x) y'(x)+x y(x) y''(x)-2 x y'(x)^2=0\) [_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1984 |
\(x y(x) y''(x)-4 x y'(x)^2+4 y(x) y'(x)=0\) [_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1985 |
\(a y'(x) \left (x y'(x)-y(x)\right )+x y(x) y''(x)=0\) [_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1986 |
\(x (y(x)+x) y''(x)+x y'(x)^2+(x-y(x)) y'(x)=y(x)\) [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1987 |
\(2 x y(x) y''(x)=x y'(x)^2-y(x) y'(x)\) [_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1988 |
\(x^2+x (2 y(x)+x) y''(x)+2 x y'(x)^2+4 (y(x)+x) y'(x)+2 y(x)=0\) [[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1989 |
\(x^2 y(x) y''(x)+\left (x y'(x)-y(x)\right )^2=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1990 |
\(x^2 y(x) y''(x)+\left (x y'(x)-y(x)\right )^2=3 y(x)^2\) [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1991 |
\(x^2 y(x) y''(x)=a x y(x) y'(x)+a y(x)^2+2 x^2 y'(x)^2\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1992 |
\(a x^2 y'(x)^2+b x y(x) y'(x)+c y(x)^2+x^2 y(x) y''(x)\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1993 |
\(x^2 (1-y(x)) y''(x)+2 x^2 y'(x)^2-2 x (1-y(x)) y'(x)+2 (1-y(x))^2 y(x)=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1994 |
\(x^2 (x-y(x)) y''(x)=\left (x y'(x)-y(x)\right )^2\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1995 |
\(x^2 (x-y(x)) y''(x)+\left (x y'(x)-y(x)\right )^2=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1996 |
\(x^2 (x-y(x)) y''(x)=a \left (x y'(x)-y(x)\right )^2\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1997 |
\(2 x^2 y(x) y''(x)=x^2 y'(x)^2-y(x)^2\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1998 |
\(2 x^2 y(x) y''(x)=x^2 y'(x)^2+2 x y(x) y'(x)-4 y(x)^2\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 1999 |
\(x^3 y(x) y''(x)+x^3 y'(x)^2+6 x^2 y(x) y'(x)+3 x y(x)^2=a\) [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2000 |
\(x (x+1)^2 y(x) y''(x)=a (x+2) y(x)^2-2 \left (x^2+1\right ) y(x) y'(x)+x (x+1)^2 y'(x)^2\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2001 |
\(8 \left (1-x^3\right ) y(x) y''(x)+4 \left (1-x^3\right ) y'(x)^2-12 x^2 y(x) y'(x)+3 x y(x)^2=0\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2002 |
\(\sqrt {a^2+x^2} \left (b y'(x)^2+y(x) y''(x)\right )=y(x) y'(x)\) [_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2003 |
\(\sqrt {a^2-x^2} \left (x y(x) y''(x)-x y'(x)^2-y(x) y'(x)\right )=b x y'(x)^2\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2004 |
\(\text {f0}(x) y(x) y''(x)+\text {f1}(x) y'(x)^2+\text {f2}(x) y(x) y'(x)+\text {f3}(x) y(x)^2=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 2005 |
\(4 f(x) y(x) y''(x)=y'(x) \left (2 f'(x)-6 f(x) y(x)^2\right )+2 y(x)^3 f'(x)+3 f(x) g(x) y(x)^2+3 f(x) y'(x)^2-f(x) y(x)^4+4 f(x)^2 y(x)\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2006 |
\(y(x)^2 y''(x)=a\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 2007 |
\(a x+y(x)^2 y''(x)+y(x) y'(x)^2=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2008 |
\(y(x)^2 y''(x)+y(x) y'(x)^2=a+b x\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2009 |
\(\left (y(x)^2+1\right ) y''(x)+(1-2 y(x)) y'(x)^2=0\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2010 |
\(\left (y(x)^2+1\right ) y''(x)=3 y(x) y'(x)^2\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2011 |
\(\left (y(x)^2+1\right ) y''(x)=(a+3 y(x)) y'(x)^2\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2012 |
\(\left (y(x)^2+1\right ) y''(x)+y'(x) \left (y'(x)^2+1\right )=0\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 2013 |
\(\left (y(x)^2+x\right ) y''(x)+2 y(x) y'(x)^2+2 y'(x)=a\) [[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2014 |
\(\left (y(x)^2+x\right ) y''(x)=2 \left (x-y(x)^2\right ) y'(x)^3-y'(x) \left (4 y(x) y'(x)+1\right )\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 2015 |
\(\left (x^2+y(x)^2\right ) y''(x)=\left (y(x)^2+1\right ) \left (x y'(x)-y(x)\right )\) [NONE] Solution method TO DO Maple ✗ |
| ODE 2016 |
\(\left (x^2+y(x)^2\right ) y''(x)=2 \left (y(x)^2+1\right ) \left (x y'(x)-y(x)\right )\) [NONE] Solution method TO DO Maple ✗ |
| ODE 2017 |
\(2 (1-y(x)) y(x) y''(x)=(1-2 y(x)) y'(x)^2\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2018 |
\(2 (1-y(x)) y(x) y''(x)=f(x) (1-y(x)) y(x) y'(x)+(1-2 y(x)) y'(x)^2\) [_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2019 |
\(2 (1-y(x)) y(x) y''(x)=(1-3 y(x)) y'(x)^2\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2020 |
\(2 (1-y(x)) y(x) y''(x)=4 y(x) y'(x) (f(x)+g(x) y(x))+(1-3 y(x)) y'(x)^2\) [NONE] Solution method TO DO Maple ✗ |
| ODE 2021 |
\(2 (1-y(x)) y(x) y''(x)=-4 y(x)^2 (1-y(x)) \left (f'(x)+f(x)^2+g'(x)-g(x)^2\right )-4 y(x) y'(x) (f(x)+g(x) y(x))-\left ((1-y(x))^3 \left (\text {F0}(x)^2-\text {G0}(x)^2 y(x)^2\right )\right )+(1-3 y(x)) y'(x)^2\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2022 |
\(3 (1-y(x)) y(x) y''(x)=2 (1-2 y(x)) y'(x)^2\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2023 |
\(4 (1-y(x)) y(x) y''(x)=3 (1-2 y(x)) y'(x)^2\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2024 |
\(x y(x)^2 y''(x)=a\) [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2025 |
\(x y(x)^2 y''(x)=\left (a-y(x)^2\right ) y'(x)+x y(x) y'(x)^2\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2026 |
\(x^2 y(x)^2 y''(x)=\left (x^2+y(x)^2\right ) \left (x y'(x)-y(x)\right )\) [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2027 |
\(\left (a^2-x^2\right ) \left (a^2-y(x)^2\right ) y''(x)+\left (a^2-x^2\right ) y(x) y'(x)^2=x \left (a^2-y(x)^2\right ) y'(x)\) [_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2028 |
\((1-y(x))^3 \left (\text {a0}+\text {a1} y(x)^2\right )+\text {a2} x (1-y(x)) y(x)^2+\text {a3} x^3 y(x)^2 (y(x)+1)+2 x^2 (1-y(x)) y(x) y''(x)-x^2 (1-3 y(x)) y'(x)^2+2 x (1-y(x)) y(x) y'(x)=0\) [NONE] Solution method TO DO Maple ✗ |
| ODE 2029 |
\(x^3 y(x)^2 y''(x)+(y(x)+x) \left (x y'(x)-y(x)\right )^3=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2030 |
\(y(x)^3 y''(x)=a^2\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 2031 |
\(y(x) \left (y(x)^2+1\right ) y''(x)+\left (1-3 y(x)^2\right ) y'(x)^2=0\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2032 |
\(2 y(x)^3 y''(x)+y(x)^2 y'(x)^2=2\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2033 |
\(2 (1-y(x)) y(x) (a-y(x)) y''(x)+(-((1-y(x)) (a-y(x)))+y(x) (a-y(x))+(1-y(x)) y(x)) y'(x)^2=\text {a0} y(x)^2 \left (1-y(x)^2\right ) (a-y(x))^2+\text {a2} y(x)^2 (a-y(x))^2+\text {a3} (1-y(x))^2 (a-y(x))^2+\text {a1} (1-y(x))^2 y(x)^2\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2034 |
\(2 (a-y(x)) (b-y(x)) (c-y(x)) y''(x)+y'(x)^2 ((a-y(x)) (b-y(x))+(a-y(x)) (c-y(x))+(b-y(x)) (c-y(x)))=\text {a0} (a-y(x))^2 (b-y(x))^2 (c-y(x))^2+2 \text {a2} (a-y(x))^2 (c-y(x))^2+\text {a3} (a-y(x))^2 (b-y(x))^2+\text {a1} (b-y(x))^2 (c-y(x))^2\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2035 |
\(2 (1-x) x (1-y(x)) (x-y(x)) y(x) y''(x)=2 (1-y(x)) \left (x^2-2 x y(x)+y(x)\right ) y(x) y'(x)+(1-x) x \left (3 y(x)^2-2 x y(x)-2 y(x)+x\right ) y'(x)^2-\left (\left (1-y(x)^2\right ) y(x)^2\right )\) [NONE] Solution method TO DO Maple ✗ |
| ODE 2036 |
\(2 (1-x) x (1-y(x)) (x-y(x)) y(x) y''(x)=f(x) ((1-y(x)) (x-y(x)) y(x))^{3/2}+2 (1-y(x)) \left (x^2-2 x y(x)+y(x)\right ) y(x) y'(x)+(1-x) x \left (3 y(x)^2-2 x y(x)-2 y(x)+x\right ) y'(x)^2-\left (\left (1-y(x)^2\right ) y(x)^2\right )\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2037 |
\(2 (1-x)^2 x^2 (1-y(x)) (x-y(x)) y(x) y''(x)=\text {a0} x (x-y(x))^2 (1-y(x))^2+\text {a1} (1-x) (x-y(x))^2 y(x)^2+(\text {a2}-1) (1-x) x y(x)^2 (1-y(x))^2+\text {a3} (x-y(x))^2 y(x)^2 (1-y(x))^2+2 (1-x) x y(x) \left (x^2-2 x y(x)+y(x)\right ) (1-y(x))^2 y'(x)+(1-x)^2 x^2 \left (3 y(x)^2-2 x y(x)-2 y(x)+x\right ) y'(x)^2\) [NONE] Solution method TO DO Maple ✗ |
| ODE 2038 |
\(b \sqrt {\left (1-y(x)^2\right ) \left (1-a^2 y(x)^2\right )} y'(x)^2+\left (1-y(x)^2\right ) \left (1-a^2 y(x)^2\right ) y''(x)+y(x) \left (-2 a^2 y(x)^2+a^2+1\right )=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2039 |
\(a^2 y(x)+\left (x^2+y(x)^2\right )^2 y''(x)=0\) [NONE] Solution method TO DO Maple ✓ |
| ODE 2040 |
\(y''(x) \left (a+2 b x+c x^2+y(x)^2\right )^2+A y(x)=0\) [NONE] Solution method TO DO Maple ✓ |
| ODE 2041 |
\(\text {f0}(y(x)) y''(x)+\text {f1}(y(x)) y'(x)^2+\text {f2}(y(x)) y'(x)+\text {f3}(y(x))=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✗ |
| ODE 2042 |
\(\sqrt {y(x)} y''(x)=a\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 2043 |
\(\sqrt {y(x)} y''(x)=2 (a+b x)\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2044 |
\(y''(x) X(x,y(x))^3=1\) [NONE] Solution method TO DO Maple ✗ |
| ODE 2045 |
\(y''(x) \left (\text {a0}+\text {a1} \sin ^2(y(x))\right )+\text {a2} y(x) \left (\text {a1} \sin ^2(y(x))+\text {a3}\right )+\text {a1} y'(x)^2+\text {a1} y'(x)^2 \sin (y(x)) \cos (y(x))=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2046 |
\(y(x) y''(x) (1-\log (y(x)))+y'(x)^2 (\log (y(x))+1)=0\) [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] Solution method TO DO Maple ✓ |
| ODE 2047 |
\(f(y(x)) y''(x)=y'(x)^2 f'(y(x))-g(x) f(y(x)) y'(x)-h(x) f(y(x))^2\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2048 |
\(f(y(x)) y''(x)=f(y(x))^2 \text {F0}\left (x,\frac {y'(x)}{f(y(x))}\right )+y'(x)^2 f'(y(x))\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2049 |
\(a y'(x)^2 f'(y(x))+f(y(x)) y''(x)+g(y(x))=0\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2050 |
\(y'(x) y''(x)=a^2 x\) [[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] Solution method TO DO Maple ✓ |
| ODE 2051 |
\(y'(x) y''(x)=x^2 y(x) y'(x)+x y(x)^2\) [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] Solution method TO DO Maple ✗ |
| ODE 2052 |
\(\left (2 x^2 y'(x)+y(x)^2\right ) y''(x)+2 (y(x)+x) y'(x)^2+x y'(x)+y(x)=0\) [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]] Solution method TO DO Maple ✗ |
| ODE 2053 |
\(a y(x)^2+x^3 y'(x) y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2054 |
\(\text {f1} y'(x) y''(x)+\text {f2} y(x) y''(x)+\text {f3} y'(x)^2+\text {f4} y(x) y'(x)+\text {f5} y(x)^2=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2055 |
\(3 y(x) y'(x) y''(x)=y'(x)^3-1\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 2056 |
\(\left (x^2+2 y(x)^2 y'(x)\right ) y''(x)+2 y(x) y'(x)^3+3 x y'(x)+y(x)=0\) [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]] Solution method TO DO Maple ✗ |
| ODE 2057 |
\(\left (x-y'(x)^2\right ) y''(x)=x^2-y'(x)\) [[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] Solution method TO DO Maple ✓ |
| ODE 2058 |
\(\left (y'(x)^2+y(x)^2\right ) y''(x)+y(x)^3=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2059 |
\(y''(x) \left (a \left (x y'(x)-y(x)\right )+y'(x)^2\right )=b\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2060 |
\(4 y(x) y'(x)^2 y''(x)=y'(x)^4+3\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 2061 |
\(y''(x) f\left (y'(x)\right )+g(y(x)) y'(x)+h(x)=0\) [[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✗ |
| ODE 2062 |
\(y''(x)^2=a+b y(x)\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 2063 |
\(y''(x)^2=a+b y'(x)^2\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2064 |
\(y''(x)^2-x y''(x)+y'(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2065 |
\(a^2 y''(x)^2=\left (y'(x)^2+1\right )^3\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2066 |
\(a x+x y''(x)^2-2 y'(x) y''(x)=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2067 |
\(\left (x y''(x)-y'(x)\right )^2=y''(x)^2+1\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2068 |
\(2 \left (x^2+1\right ) y''(x)^2+2 \left (x-y'(x)\right ) y'(x)-x \left (4 y'(x)+x\right ) y''(x)=2 y(x)\) [NONE] Solution method TO DO Maple ✗ |
| ODE 2069 |
\(3 x^2 y''(x)^2+4 y'(x)^2-2 \left (3 x y'(x)+y(x)\right ) y''(x)=0\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2070 |
\((2-9 x) x^2 y''(x)^2+6 y(x) y''(x)-6 (1-6 x) x y'(x) y''(x)=36 x y'(x)^2\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2071 |
\(\text {f0} y''(x)^2+\text {f1} y'(x) y''(x)+\text {f2} y(x) y''(x)+\text {g0} y'(x)^2+\text {g1} y(x) y'(x)+h y(x)^2=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2072 |
\(y(x) y''(x)+4 y(x) y'(x)^3-y'(x)^2=0\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] Solution method TO DO Maple ✓ |
| ODE 2073 |
\(\left (y(x) y''(x)+y'(x)^2+1\right )^2=\left (y'(x)^2+1\right )^3\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 2074 |
\(y''(x)^2 \left (a^2-b^2 y(x)^2\right )+y'(x)^2 \left (1-b^2 y'(x)^2\right )+2 b^2 y(x) y'(x)^2 y''(x)=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2075 |
\(\left (x^2 y(x) y''(x)+x^2 \left (-y'(x)^2\right )+y(x)^2\right )^2=4 x y(x) \left (x y'(x)-y(x)\right )^3\) [[_2nd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2076 |
\(y''(x)^3=12 y'(x) \left (x y''(x)-2 y'(x)\right )\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2077 |
\(32 y''(x) \left (x y''(x)-y'(x)\right )^3+\left (2 y(x) y''(x)-y'(x)^2\right )^3=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✗ |
| ODE 2078 |
\(f\left (y''(x)\right )+x y''(x)=y'(x)\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2079 |
\(y'(x) f\left (\frac {y''(x)}{y'(x)}\right )=y'(x)^2-y(x) y''(x)\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2080 |
\(f\left (y''(x),y'(x)-x y''(x),\frac {1}{2} x^2 y''(x)-x y'(x)+y(x)\right )=0\) [NONE] Solution method TO DO Maple ✓ |
| ODE 2081 |
\(f\left (x,y''(x)\right )=0\) [[_2nd_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 2082 |
\(f\left (y(x),y''(x)\right )=0\) [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] Solution method TO DO Maple ✓ |
| ODE 2083 |
\(f\left (y'(x),y''(x)\right )=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✗ |
| ODE 2084 |
\(f\left (x,y'(x),y''(x)\right )=0\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✗ |
| ODE 2085 |
\(f\left (y(x),y'(x),y''(x)\right )=0\) [[_2nd_order, _missing_x]] Solution method TO DO Maple ✗ |
| ODE 2086 |
\(y'''(x)=0\) [[_3rd_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 2087 |
\(y'''(x)=\cos (x)+1\) [[_3rd_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 2088 |
\(y'''(x)+\sin (x)=0\) [[_3rd_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 2089 |
\(y'''(x)=\sin ^3(x)\) [[_3rd_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 2090 |
\(y'''(x)=y(x)\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2091 |
\(y'''(x)=x^2+y(x)\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2092 |
\(y'''(x)=y(x)+e^x x+\cos ^2(x)\) [[_3rd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2093 |
\(y'''(x)+a y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2094 |
\(y'''(x)=x y(x)\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2095 |
\(y'''(x)+y'(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2096 |
\(y'''(x)=y'(x)\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2097 |
\(y'''(x)+y'(x)=x^3+\cos (x)\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2098 |
\(y'''(x)-2 y'(x)+4 y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2099 |
\(y'''(x)-2 y'(x)+4 y(x)=e^x \cos (x)\) [[_3rd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2100 |
\(y'''(x)-3 y'(x)+2 y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2101 |
\(y'''(x)-3 y'(x)+2 y(x)=3 e^x\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2102 |
\(y'''(x)-3 y'(x)+2 y(x)=e^x x^2\) [[_3rd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2103 |
\(y'''(x)-4 y'(x)=x^2-3 e^{2 x}\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2104 |
\(y'''(x)-7 y'(x)+6 y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2105 |
\(y'''(x)=a^2 y(x)\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2106 |
\(y'''(x)+2 x y'(x)+y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2107 |
\(y'''(x)+2 a x y'(x)+a y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2108 |
\(y'''(x)+y(x) f'(x)+2 f(x) y'(x)=0\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2109 |
\(y'''(x)-y''(x)+y'(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2110 |
\(y'''(x)-y''(x)+y'(x)+y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2111 |
\(y'''(x)+y''(x)+y'(x)-3 y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2112 |
\(y'''(x)-y''(x)-2 y'(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2113 |
\(y'''(x)-y''(x)-2 y'(x)=e^{-x}\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2114 |
\(y'''(x)+y''(x)+4 y'(x)+4 y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2115 |
\(y'''(x)+y''(x)+2 y'(x)+4 y(x)=\sin (2 x)\) [[_3rd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2116 |
\(y'''(x)+y''(x)-7 y'(x)-15 y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2117 |
\(y'''(x)+2 y''(x)+y'(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2118 |
\(y'''(x)+2 y''(x)+y'(x)=(x-1) x\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2119 |
\(y'''(x)-2 y''(x)+y'(x)=e^x\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2120 |
\(y'''(x)-2 y''(x)-y'(x)+2 y(x)=\sinh (x)\) [[_3rd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2121 |
\(y'''(x)-2 y''(x)-3 y'(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2122 |
\(y'''(x)-2 y''(x)-3 y'(x)=3 x^2+\sin (x)\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2123 |
\(y'''(x)-2 y''(x)-3 y'(x)=3 x^2+e^{-x}\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2124 |
\(y'''(x)-2 y''(x)+3 y'(x)+10 y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2125 |
\(y'''(x)-a^2 y'(x)+2 a^2 y(x)-2 y''(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2126 |
\(y'''(x)-a^2 y'(x)+2 a^2 y(x)-2 y''(x)=\sinh (x)\) [[_3rd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2127 |
\(y'''(x)-3 y''(x)+4 y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2128 |
\(y'''(x)+3 y''(x)-y'(x)-3 y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2129 |
\(y'''(x)-3 y''(x)-y'(x)+3 y(x)=x^2\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2130 |
\(y'''(x)+3 y''(x)-y'(x)-3 y(x)=\cosh (x)\) [[_3rd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2131 |
\(y'''(x)+3 y''(x)+3 y'(x)+y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2132 |
\(y'''(x)+3 y''(x)+3 y'(x)+y(x)=e^{-x} x\) [[_3rd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2133 |
\(y'''(x)-3 y''(x)+3 y'(x)-y(x)=x \left (1-e^x x^2\right )\) [[_3rd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2134 |
\(y'''(x)+3 y''(x)+3 y'(x)+y(x)=e^{-x} \left (2-x^2\right )\) [[_3rd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2135 |
\(y'''(x)-3 y''(x)+4 y'(x)-2 y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2136 |
\(y'''(x)-3 y''(x)+4 y'(x)-2 y(x)=e^x+\cos (x)\) [[_3rd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2137 |
\(y'''(x)-4 y''(x)+5 y'(x)-2 y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2138 |
\(y'''(x)-4 y''(x)+5 y'(x)-2 y(x)=x\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2139 |
\(y'''(x)-4 y''(x)+6 y'(x)-4 y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2140 |
\(y'''(x)-6 y''(x)+9 y'(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2141 |
\(y'''(x)-6 y''(x)+12 y'(x)-8 y(x)=e^{2 x} x^2\) [[_3rd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2142 |
\(y'''(x)+a^3 (-y(x))+3 a^2 y'(x)-3 a y''(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2143 |
\(y'''(x)+a^3 (-y(x))+3 a^2 y'(x)-3 a y''(x)=e^{a x}\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2144 |
\(y'''(x)=a y''(x)\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2145 |
\(y'''(x)+\text {a1} y''(x)+\text {a2} y'(x)+\text {a3} y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2146 |
\(y'''(x)-2 \left (-2 a-4 x^2+1\right ) y'(x)-8 a x y(x)-6 x y''(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2147 |
\(y'''(x)+a^3 x^3 y(x)+3 a^2 x^2 y'(x)+3 a x y''(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2148 |
\(y'''(x)+x^2 \left (-y''(x)\right )+2 x y'(x)-2 y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2149 |
\(y'''(x)+y''(x) (2 \cot (x)+\csc (x))-y'(x)=\cot (x)\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2150 |
\(y'''(x)-\sin (x) y''(x)-2 \cos (x) y'(x)+y(x) \sin (x)=\log (x)\) [[_3rd_order, _fully, _exact, _linear]] Solution method TO DO Maple ✓ |
| ODE 2151 |
\(y'''(x)+y'(x) \left (2 f'(x)^2+f'(x)+4 g(x)\right )+2 y(x) \left (2 f(x) g(x)+g'(x)\right )+3 f(x) y''(x)=0\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2152 |
\(y'''(x)+f(x) y''(x)+f(x) y(x)+y'(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2153 |
\(4 y'''(x)-3 y'(x)+y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2154 |
\(4 y'''(x)-8 y''(x)-11 y'(x)-3 y(x)=0\) [[_3rd_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2155 |
\(4 y'''(x)-8 y''(x)-11 y'(x)-3 y(x)+18 e^x=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2156 |
\(x y'''(x)=2\) [[_3rd_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 2157 |
\(x y'''(x)+3 y'(x)+x y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2158 |
\(x y'''(x)-y''(x)+x y'(x)-y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2159 |
\(x y'''(x)-y''(x)-x y'(x)+y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2160 |
\(x y'''(x)-y''(x)-x y'(x)+y(x)=1-x^2\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2161 |
\(x y'''(x)+x^2 (-y(x))+3 y''(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2162 |
\(x y'''(x)-\left (3-x^2\right ) y''(x)+4 x y'(x)+2 y(x)=0\) [[_3rd_order, _fully, _exact, _linear]] Solution method TO DO Maple ✓ |
| ODE 2163 |
\((1-2 x) y'''(x)-(x+4) y''(x)-2 y'(x)=0\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2164 |
\(x^2 y'''(x)+a x^2 y(x)-6 y'(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2165 |
\(x^2 y'''(x)+2 x y''(x)=a\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2166 |
\(x^2 y'''(x)+\left (x^2+2\right ) y'(x)+4 x y''(x)+3 x y(x)=f(x)\) [[_3rd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2167 |
\(x^2 y'''(x)+5 x y''(x)+4 y'(x)=\log (x)\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2168 |
\(x^2 y'''(x)+6 x y''(x)+6 y'(x)=0\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2169 |
\(x^2 y'''(x)+a x^2 y(x)+6 x y''(x)+6 y'(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2170 |
\(x^2 y'''(x)-2 (n+1) x y''(x)+6 n y'(x)=0\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2171 |
\(x^2 y'''(x)+\left (6-2 x^3\right ) y'(x)+2 x^3 y(x)+\left (6-x^2\right ) x y''(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 2172 |
\(\left (x^2+1\right ) y'''(x)+8 x y'(x)+10 y'(x)=0\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2173 |
\(\left (x^2+2\right ) y'''(x)+\left (x^2+2\right ) y'(x)-2 x y''(x)-2 x y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2174 |
\(\left (x^2-2 x+2\right ) y'''(x)+x^2 \left (-y''(x)\right )+2 x y'(x)-2 y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2175 |
\((x+2)^2 y'''(x)+(x+2) y''(x)+y'(x)=0\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2176 |
\(4 x^2 y'''(x)+8 x y''(x)+y'(x)=0\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2177 |
\(x (\text {a0}+\text {b0} x) y'''(x)+(\text {a1}+\text {b1} x) y''(x)+x y'(x)+y(x)=f(x)\) [[_3rd_order, _exact, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2178 |
\(x^3 y'''(x)=a\) [[_3rd_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 2179 |
\(x^3 y'''(x)+x y'(x)-y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2180 |
\(x^3 y'''(x)+x y'(x)-y(x)=x \log (x)\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2181 |
\(x^3 y'''(x)-x^2 y''(x)+2 x y'(x)-2 y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2182 |
\(x^3 y'''(x)-x^2 y''(x)+2 x y'(x)-2 y(x)=x \left (x^2+3\right )\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2183 |
\(x^3 y'''(x)+x^2 y''(x)+3 x y'(x)-8 y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2184 |
\(x^3 y'''(x)-x^2 y''(x)+x y'(x)=0\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2185 |
\(x^3 y'''(x)+2 x^2 y''(x)+2 y(x)=0\) [[_3rd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 2186 |
\(x^3 y'''(x)+2 x^2 y''(x)-x y'(x)+y(x)=0\) [[_3rd_order, _exact, _linear, _homogeneous]] Solution method TO DO Maple ✓ |
| ODE 2187 |
\(x^3 y'''(x)+3 x^2 y''(x)=a\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2188 |
\(x^3 y'''(x)+3 x^2 y''(x)-2 x y'(x)+2 y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2189 |
\(x^3 y'''(x)-3 x^2 y''(x)+7 x y'(x)-8 y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2190 |
\(x^3 y'''(x)+\left (1-a^2\right ) x y'(x)+3 x^2 y''(x)=0\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2191 |
\(x^3 y'''(x)+4 x^2 y''(x)-8 x y'(x)+8 y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2192 |
\(x^3 y'''(x)-4 x^2 y''(x)+\left (x^2+8\right ) x y'(x)-2 \left (x^2+4\right ) y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2193 |
\(x^3 y'''(x)-\left (12-a x^3\right ) y(x)+6 x^2 y''(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2194 |
\(x^3 y'''(x)+x^2 \log (x) y''(x)+2 x y'(x)-y(x)=2 x^3\) [[_3rd_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2195 |
\(\left (x^3+1\right ) y'''(x)+9 x^2 y''(x)+18 x y'(x)+6 y(x)=0\) [[_3rd_order, _fully, _exact, _linear]] Solution method TO DO Maple ✓ |
| ODE 2196 |
\(x \left (x^2+1\right ) y'''(x)+3 \left (2 x^2+1\right ) y''(x)-12 y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2197 |
\(x \left (1-x^2\right ) y'''(x)+\left (3-8 x^2\right ) y''(x)-14 x y'(x)-4 y(x)=0\) [[_3rd_order, _fully, _exact, _linear]] Solution method TO DO Maple ✓ |
| ODE 2198 |
\(x \left (x^2-2 x+2\right ) y'''(x)+\left (-x^3+3 x^2-6 x+6\right ) y''(x)=0\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2199 |
\((x+1)^3 y'''(x)+(x+1)^2 y''(x)+3 (x+1) y'(x)-8 y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2200 |
\(x^2 (y(x)+3) y'''(x)-3 (x+2) x y''(x)+6 (x+1) y'(x)-6 y(x)=0\) [NONE] Solution method TO DO Maple ✗ |
| ODE 2201 |
\(4 x^3 y'''(x)+x y'(x)-y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2202 |
\((1-2 x)^3 y'''(x)+(1-2 x) y'(x)+2 y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2203 |
\(x^4 y'''(x)+2 x^3 y''(x)+2 x y(x)=10 \left (x^2+1\right )\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2204 |
\(x^4 y'''(x)+2 x^3 y''(x)-x^2 y'(x)+x y(x)=1\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2205 |
\(\left (x^2+1\right ) x^2 y'''(x)+8 x^3 y''(x)+10 x^2 y'(x)=3 x^2+2 x^2 \log (x)-1\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2206 |
\((x+1) x^3 y'''(x)-2 (2 x+1) x^2 y''(x)+2 (5 x+2) x y'(x)-4 (3 x+1) y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2207 |
\(4 x^4 y'''(x)-4 x^3 y''(x)+4 x^2 y'(x)=1\) [[_3rd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2208 |
\(\left (x^2+1\right ) x^3 y'''(x)-2 \left (2 x^2+1\right ) x^2 y''(x)+2 \left (5 x^2+2\right ) x y'(x)-4 \left (3 x^2+1\right ) y(x)=0\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2209 |
\((a-x)^3 (b-x)^3 y'''(x)=c y(x)\) [[_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2210 |
\((x+\sin (x)) y'''(x)+3 (\cos (x)+1) y''(x)-3 \sin (x) y'(x)-y(x) \cos (x)+\sin (x)=0\) [[_3rd_order, _fully, _exact, _linear]] Solution method TO DO Maple ✓ |
| ODE 2211 |
\(y''''(x)=0\) [[_high_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 2212 |
\(y''''(x)=x \cos (x)\) [[_high_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 2213 |
\(y''''(x)+4 e^{-x} \cos (x)=0\) [[_high_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 2214 |
\(y''''(x)=y(x)+\cos (x)\) [[_high_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2215 |
\(y''''(x)=y(x)+e^x \cos (x)\) [[_high_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2216 |
\(y''''(x)+a y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2217 |
\(y''''(x)=a^4 y(x)+x^3\) [[_high_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2218 |
\(y''''(x)+y''(x)+y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2219 |
\(y''''(x)+2 y''(x)+y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2220 |
\(y''''(x)-2 y''(x)+y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2221 |
\(y''''(x)+2 y''(x)+y(x)=\cos (x)\) [[_high_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2222 |
\(y''''(x)-2 y''(x)+y(x)=\cos (x)\) [[_high_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2223 |
\(y''''(x)+2 y''(x)+y(x)=24 x \sin (x)\) [[_high_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2224 |
\(y''''(x)-2 y''(x)+y(x)=e^x+4\) [[_high_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2225 |
\(y''''(x)-2 y''(x)-8 y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2226 |
\(y''''(x)+3 y''(x)-4 y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2227 |
\(y''''(x)+5 y''(x)+6 y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2228 |
\(y''''(x)-12 y''(x)+27 y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2229 |
\(y''''(x)+a^2 y''(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2230 |
\(y''''(x)+a^4 y(x)+2 a^2 y''(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2231 |
\(y''''(x)+a^4 y(x)+2 a^2 y''(x)=\cosh (a x)\) [[_high_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2232 |
\(y''''(x)+\left (a^2+b^2\right ) y''(x)+a^2 b^2 y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2233 |
\(y''''(x)+3 y(x) \left (f''(x)+3 f(x)^2\right )+10 f'(x) y'(x)+10 f(x) y''(x)=0\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2234 |
\(-y'''(x)+y''''(x)-3 y''(x)+5 y'(x)-2 y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2235 |
\(-y'''(x)+y''''(x)-3 y''(x)+5 y'(x)-2 y(x)=e^{3 x}\) [[_high_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2236 |
\(-2 y'''(x)+y''''(x)+y(x)^2=0\) [[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 2237 |
\(-2 y'''(x)+y''''(x)+y(x)^2=x^3\) [NONE] Solution method TO DO Maple ✗ |
| ODE 2238 |
\(2 y'''(x)+y''''(x)-2 y'(x)-y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2239 |
\(-2 y'''(x)+y''''(x)+2 y''(x)-2 y'(x)+y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2240 |
\(2 y'''(x)+y''''(x)+3 y''(x)+2 y'(x)+y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2241 |
\(2 y'''(x)+y''''(x)-3 y''(x)-4 y'(x)+4 y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2242 |
\(-3 y'''(x)+y''''(x)+y''(x)-y'(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2243 |
\(-4 y'''(x)+y''''(x)+6 y''(x)-4 y'(x)+y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2244 |
\(-4 y'''(x)+y''''(x)+12 y''(x)-16 y'(x)+16 y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2245 |
\(4 a x y'''(x)+y''''(x)+a^4 x^4 y(x)+4 a^3 x^3 y'(x)+6 a^2 x^2 y''(x)=0\) [[_high_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2246 |
\(2 \left (y''''(x)+\left (a^2+b^2\right ) y''(x)+a^2 b^2 y(x)\right )=\cos (a x)+\cos (b x)\) [[_high_order, _linear, _nonhomogeneous]] Solution method TO DO Maple ✓ |
| ODE 2247 |
\(-12 y'''(x)+4 y''''(x)+11 y''(x)-3 y'(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2248 |
\(3 y'''(x)+x y''''(x)=0\) [[_high_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2249 |
\(5 y'''(x)+x y''''(x)=0\) [[_high_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2250 |
\(x^2 y''''(x)=2 y'''(x)\) [[_high_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2251 |
\(x^2 y''''(x)=2 y''(x)\) [[_high_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2252 |
\(x^2 y''''(x)+4 x y'''(x)+2 y''(x)=0\) [[_high_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2253 |
\(x^2 y''''(x)+6 x y'''(x)+6 y''(x)=0\) [[_high_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2254 |
\(x^2 y''''(x)+8 x y'''(x)+12 y''(x)=0\) [[_high_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2255 |
\(x^2 y''''(x)+8 x y'''(x)+a^2 (-y(x))+12 y''(x)=0\) [[_high_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2256 |
\((a+x)^2 y''''(x)=1\) [[_high_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 2257 |
\(32 x (a-b+2) y'''(x)+16 x^2 y''''(x)+16 (a-b+1) (a-b+2) y''(x)+c^4 (-y(x))=0\) [[_high_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2258 |
\(x^3 y''''(x)+2 x^2 y'''(x)+a^4 \left (-x^3\right ) y(x)-x y''(x)=0\) [[_high_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2259 |
\(x^3 y''''(x)+6 x^2 y'''(x)+6 x y''(x)=0\) [[_high_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2260 |
\(x^2 (a+b+c+3) y'''(x)+x^3 y''''(x)+x (a b+a c+a+b c+b+c+1) y''(x)-y'(x) (x-a b c)-k y(x)=0\) [[_high_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2261 |
\(x^4 y''''(x)+6 x^3 y'''(x)+4 x^2 y''(x)-2 x y'(x)-4 y(x)=0\) [[_high_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2262 |
\(x^4 y''''(x)+6 x^3 y'''(x)+9 x^2 y''(x)+3 x y'(x)+y(x)=0\) [[_high_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2263 |
\(x^4 y''''(x)+8 x^3 y'''(x)+12 x^2 y''(x)=0\) [[_high_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2264 |
\(x^4 y''''(x)+8 x^3 y'''(x)+a y(x)+12 x^2 y''(x)=0\) [[_high_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2265 |
\(\text {A1} x^3 y'''(x)+x^4 y''''(x)+\text {A2} x^2 y''(x)+\text {A3} x y'(x)+\text {A4} y(x)=0\) [[_high_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2266 |
\(16 a^4 x^4 y''''(x)-32 (1-2 a) a^2 x^3 y'''(x)+16 (1-2 a) (1-a) a^2 x^2 y''(x)-b^4 x^{2/a} y(x)=0\) [[_high_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2267 |
\(4 \left (e^x+2\right ) y'''(x)+\left (2 x+e^x\right ) y''''(x)+6 e^x y''(x)+4 e^x y'(x)+e^x y(x)=0\) [[_high_order, _fully, _exact, _linear]] Solution method TO DO Maple ✓ |
| ODE 2268 |
\(-y'''(x)+y'''''(x)-2 y''(x)+2 y'(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2269 |
\(2 y'''(x)+y'''''(x)+y'(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2270 |
\(2 y'''(x)+y'''''(x)+y'(x)=a x+b \cos (x)+c \sin (x)\) [[_high_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2271 |
\(y''''''(x)=0\) [[_high_order, _quadrature]] Solution method TO DO Maple ✓ |
| ODE 2272 |
\(y''''''(x)+a y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2273 |
\(2 y'''(x)+y''''''(x)+y(x)=0\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2274 |
\(y''''''''(x)=y(x)\) [[_high_order, _missing_x]] Solution method TO DO Maple ✓ |
| ODE 2275 |
\(y''''''''(x)-2 y''''+y(x)=0\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2276 |
\(\frac {\partial ^{2 n}y(x)}{\partial x^{2 n}}=a^{2 n} y(x)\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2277 |
\(x^n \frac {\partial ^{2 n}y(x)}{\partial x^{2 n}}=y(x)\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2278 |
\(x^{n+\frac {1}{2}} \frac {\partial ^{2 n+1}y(x)}{\partial x^{2 n+1}}=y(x)\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2279 |
\(y^{(n)}(x)=e^x x\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2280 |
\(a m x^{m-1} y(x)+a x^m y'(x)+y^{(n)}(x)=0\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2281 |
\((a-x)^n (b-x)^n y^{(n)}(x)=c y(x)\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2282 |
\(y'''(x)=y'(x) \left (y'(x)+1\right )\) [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] Solution method TO DO Maple ✓ |
| ODE 2283 |
\(y'''(x)+y'(x)^2-y(x) y'(x)=0\) [[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 2284 |
\(y'''(x)+a y(x) y''(x)=0\) [[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 2285 |
\(x^2 y'''(x)+x y''(x)-(1-2 x y(x)) y'(x)+y(x)^2=f(x)\) [[_3rd_order, _exact, _nonlinear]] Solution method TO DO Maple ✗ |
| ODE 2286 |
\(x^2 y'''(x)-x (1-y(x)) y''(x)+x y'(x)^2+(1-y(x)) y'(x)=0\) [[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] Solution method TO DO Maple ✓ |
| ODE 2287 |
\(y(x) y'''(x)+y(x)^3 y'(x)-y'(x) y''(x)=0\) [[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2288 |
\((a+y(x)) y'''(x)+3 y'(x) y''(x)=0\) [[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] Solution method TO DO Maple ✓ |
| ODE 2289 |
\(x^3 y(x) y'''(x)+3 x^3 y'(x) y''(x)+9 x^2 y(x) y''(x)+9 x^2 y'(x)^2+18 x y(x) y'(x)+3 y(x)^2=0\) [[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2290 |
\(\left (y(x)^2+x\right ) y'''(x)+3 y''(x)+2 y'(x)^3+6 y(x) y'(x) y''(x)=0\) [[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2291 |
\(4 y(x)^2 y'''(x)+15 y'(x)^3-18 y(x) y'(x) y''(x)=0\) [[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2292 |
\(9 y(x)^2 y'''(x)+40 y'(x)^3-45 y(x) y'(x) y''(x)=0\) [[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2293 |
\(y'(x) y'''(x)+y'(x)^2=2 y''(x)^2\) [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2294 |
\(y'(x) y''(x)=a x y'(x)^5+3 y''(x)^2\) [[_2nd_order, _missing_y]] Solution method TO DO Maple ✓ |
| ODE 2295 |
\(2 y'(x) y'''(x)=2 y''(x)^2\) [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] Solution method TO DO Maple ✓ |
| ODE 2296 |
\(\left (y'(x)^2+1\right ) y'''(x)=3 y'(x) y''(x)^2\) [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] Solution method TO DO Maple ✓ |
| ODE 2297 |
\(\left (y'(x)^2+1\right ) y'''(x)=y''(x)^2 \left (a+3 y'(x)\right )\) [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] Solution method TO DO Maple ✓ |
| ODE 2298 |
\(y'(x)^3 y'''(x)=1\) [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] Solution method TO DO Maple ✓ |
| ODE 2299 |
\(y''(x) y'''(x)=2\) [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] Solution method TO DO Maple ✓ |
| ODE 2300 |
\(y''(x) y'''(x)=a \sqrt {b^2 y''(x)^2+1}\) [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] Solution method TO DO Maple ✓ |
| ODE 2301 |
\(2 x y''(x) y'''(x)=y''(x)^2-a^2\) [[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] Solution method TO DO Maple ✓ |
| ODE 2302 |
\(\left (1-x^2\right ) \left (y'''(x)\right )^2+2 x y''(x) y'''(x)-y''(x)^2+1=0\) [[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2303 |
\(\sqrt {y''(x)^2+1} \left (1-y'''(x)\right )=y''(x) y'''(x)\) [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] Solution method TO DO Maple ✓ |
| ODE 2304 |
\(3 y''(x) y''''(x)=5 \left (y'''(x)\right )^2\) [[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]] Solution method TO DO Maple ✓ |
| ODE 2305 |
\(-4 y'(x) \left (y'''(x)\right )^2+3 y'(x) y''(x) y''''(x)-3 y''(x)^3=0\) [[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] Solution method TO DO Maple ✗ |
| ODE 2306 |
\(-45 y''(x) y'''(x) y''''(x)+9 y''(x)^2 y'''''(x)+40 \left (y'''(x)\right )^3=0\) [[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] Solution method TO DO Maple ✓ |
| ODE 2307 |
\(y^{(n)}(x)=f(x)\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2308 |
\(y^{(n)}(x)=f\left (\frac {\partial ^{n-2}y(x)}{\partial x^{n-2}}\right )\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2309 |
\(y^{(n)}(x)=f\left (\frac {\partial ^{n-1}y(x)}{\partial x^{n-1}}\right )\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2310 |
\(y^{(n)}(x) \frac {\partial ^{n-2}y(x)}{\partial x^{n-2}}=\left (\frac {\partial ^{n-1}y(x)}{\partial x^{n-1}}\right )^2\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2311 |
\(f\left (x,y^{(n)}(x)\right )=0\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2312 |
\(f\left (x,\frac {\partial ^{n-1}y(x)}{\partial x^{n-1}},y^{(n)}(x)\right )=0\) odeadvisor timed out Solution method TO DO Maple ✗ |
| ODE 2313 |
\(f\left (\frac {\partial ^{n-2}y(x)}{\partial x^{n-2}},\frac {\partial ^{n-1}y(x)}{\partial x^{n-1}},y^{(n)}(x)\right )=0\) odeadvisor timed out Solution method TO DO Maple ✗ |