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.
| | |
| # |
result |
| ODE 1 |
\(y'(x)=a f(x)\) Solution method Separable ODE, Dependent variable missing Maple ✓ |
| ODE 2 |
\(y'(x)=y(x)+x+\sin (x)\) Solution method Linear ODE Maple ✓ |
| ODE 3 |
\(y'(x)=x^2+2 y(x)+3 \cosh (x)\) Solution method Linear ODE Maple ✓ |
| ODE 4 |
\(y'(x)=a+b x+c y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 5 |
\(y'(x)=a \cos (b x+c)+k y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 6 |
\(y'(x)=a \sin (b x+c)+k y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 7 |
\(y'(x)=a+b e^{k x}+c y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 8 |
\(y'(x)=x \left (x^2-y(x)\right )\) Solution method Linear ODE Maple ✓ |
| ODE 9 |
\(y'(x)=x \left (a y(x)+e^{-x^2}\right )\) Solution method Linear ODE Maple ✓ |
| ODE 10 |
\(y'(x)=x^2 \left (a x^3+b y(x)\right )\) Solution method Linear ODE Maple ✓ |
| ODE 11 |
\(y'(x)=a x^n y(x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 12 |
\(y'(x)=y(x) \cos (x)+\sin (x) \cos (x)\) Solution method Linear ODE Maple ✓ |
| ODE 13 |
\(y'(x)=y(x) \cos (x)+e^{\sin (x)}\) Solution method Linear ODE Maple ✓ |
| ODE 14 |
\(y'(x)=y(x) \cot (x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 15 |
\(y'(x)=1-y(x) \cot (x)\) Solution method Linear ODE Maple ✓ |
| ODE 16 |
\(y'(x)=x \csc (x)-y(x) \cot (x)\) Solution method Linear ODE Maple ✓ |
| ODE 17 |
\(y'(x)=y(x) (\cot (x)+2 \csc (2 x))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 18 |
\(y'(x)=\sec (x)-y(x) \cot (x)\) Solution method Linear ODE Maple ✓ |
| ODE 19 |
\(y'(x)=y(x) \cot (x)+e^x \sin (x)\) Solution method Linear ODE Maple ✓ |
| ODE 20 |
\(y'(x)+2 y(x) \cot (x)+\csc (x)=0\) Solution method Linear ODE Maple ✓ |
| ODE 21 |
\(y'(x)=4 x \csc (x) \sec ^2(x)-2 y(x) \cot (2 x)\) Solution method Linear ODE Maple ✓ |
| ODE 22 |
\(y'(x)=2 \left (\cos (2 x) \cot ^2(x)-y(x) \csc (2 x)\right )\) Solution method Linear ODE Maple ✓ |
| ODE 23 |
\(y'(x)=4 x \csc (x) \left (y(x)+\sin ^3(x)\right )\) Solution method Linear ODE Maple ✓ |
| ODE 24 |
\(y'(x)=4 x \csc (x) \left (y(x)-\tan ^2(x)+1\right )\) Solution method Linear ODE Maple ✓ |
| ODE 25 |
\(y'(x)=y(x) \sec (x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 26 |
\(y'(x)+\tan (x)=(1-y(x)) \sec (x)\) Solution method Linear ODE Maple ✓ |
| ODE 27 |
\(y'(x)=y(x) \tan (x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 28 |
\(y'(x)=y(x) \tan (x)+\cos (x)\) Solution method Linear ODE Maple ✓ |
| ODE 29 |
\(y'(x)=\cos (x)-y(x) \tan (x)\) Solution method Linear ODE Maple ✓ |
| ODE 30 |
\(y'(x)=\sec (x)-y(x) \tan (x)\) Solution method Linear ODE Maple ✓ |
| ODE 31 |
\(y'(x)=y(x) \tan (x)+\sin (2 x)\) Solution method Linear ODE Maple ✓ |
| ODE 32 |
\(y'(x)=\sin (2 x)-y(x) \tan (x)\) Solution method Linear ODE Maple ✓ |
| ODE 33 |
\(y'(x)=2 y(x) \tan (x)+\sin (x)\) Solution method Linear ODE Maple ✓ |
| ODE 34 |
\(y'(x)=2 (y(x) \tan (2 x)+\sec (2 x)+1)\) Solution method Linear ODE Maple ✓ |
| ODE 35 |
\(y'(x)=3 y(x) \tan (x)+\csc (x)\) Solution method Linear ODE Maple ✓ |
| ODE 36 |
\(y'(x)=y(x) (a+\sin (\log (x))+\cos (\log (x)))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 37 |
\(y'(x)=6 e^{2 x}-y(x) \tanh (x)\) Solution method Linear ODE Maple ✓ |
| ODE 38 |
\(y'(x)=y(x) f'(x)+f(x) f'(x)\) Solution method Linear ODE Maple ✓ |
| ODE 39 |
\(y'(x)=f(x)+g(x) y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 40 |
\(y'(x)=x^2-y(x)^2\) Solution method Series solution to \(y'(x)=f(x,y(x))\), case \(f(x,y)\) analytic Maple ✓ |
| ODE 41 |
\(f(x)^2+y'(x)=f'(x)+y(x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 42 |
\(y'(x)-x+1=y(x) (y(x)+x)\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 43 |
\(y'(x)=(y(x)+x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 44 |
\(y'(x)=(x-y(x))^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 45 |
\(y'(x)=(x-y(x))^2+3 (y(x)-x+1)\) Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\) Maple ✓ |
| ODE 46 |
\(y'(x)=-\left (x^2+1\right ) y(x)+y(x)^2+2 x\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 47 |
\(y'(x)=x \left (x^3+2\right )-\left (2 x^2-y(x)\right ) y(x)\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 48 |
\(y'(x)=x \left (2-x^3\right )+\left (2 x^2-y(x)\right ) y(x)+1\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 49 |
\(y'(x)=\cos (x)-y(x) (\sin (x)-y(x))\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 50 |
\(y'(x)=y(x) (y(x)+\sin (2 x))+\cos (2 x)\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 51 |
\(y'(x)=x f(x) y(x)+f(x)+y(x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 52 |
\(y'(x)=(-4 y(x)+x+3)^2\) Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\) Maple ✓ |
| ODE 53 |
\(y'(x)=(9 y(x)+4 x+1)^2\) Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\) Maple ✓ |
| ODE 54 |
\(y'(x)=3 \left (a+b y(x)^2+b x\right )\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 55 |
\(y'(x)=a+b y(x)^2\) Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 56 |
\(y'(x)=a x+b y(x)^2\) Solution method Riccati ODE, Main form Maple ✓ |
| ODE 57 |
\(y'(x)=a+b x+c y(x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 58 |
\(y'(x)=a x^{n-1}+b x^{2 n}+c y(x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 59 |
\(y'(x)=a x^2+b y(x)^2\) Solution method Riccati ODE, Main form Maple ✓ |
| ODE 60 |
\(y'(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2\) Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 61 |
\(y'(x)=a y(x)+b y(x)^2+f(x)\) Solution method Riccati ODE, Generalized ODE Maple ✗ |
| ODE 62 |
\(y'(x)=a (x-y(x)) y(x)+1\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 63 |
\(y'(x)=a y(x)^2+f(x)+g(x) y(x)\) Solution method Riccati ODE, Generalized ODE Maple ✗ |
| ODE 64 |
\(y'(x)=x y(x) (y(x)+3)\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 65 |
\(y'(x)=-x^3+\left (2 x^2+1\right ) y(x)-x y(x)^2-x+1\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 66 |
\(y'(x)=x \left (x^2 y(x)-y(x)^2+2\right )\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 67 |
\(y'(x)=-(1-x) y(x)^2+(1-2 x) y(x)+x\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 68 |
\(y'(x)=a x y(x)^2\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 69 |
\(y'(x)=x^n \left (a+b y(x)^2\right )\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 70 |
\(y'(x)=a x^m+b x^n y(x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 71 |
\(y'(x)=y(x) (a+b y(x) \cos (k x))\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 72 |
\(y'(x)=\sin (x) \left (2 \sec ^2(x)-y(x)\right )\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 73 |
\(y'(x)+4 \csc (x)=y(x)^2 \sin (x)+y(x) (3-\cot (x))\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 74 |
\(y'(x)=y(x) \sec (x)+(\sin (x)-1)^2\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 75 |
\(y'(x)+\left (1-y(x)^2\right ) \tan (x)=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 76 |
\(y'(x)=f(x)+g(x) y(x)+h(x) y(x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✗ |
| ODE 77 |
\(y'(x)=f(x) \left (a+b y(x)+c y(x)^2\right )\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 78 |
\(y(x)^2 (a x+y(x))+y'(x)\) Solution method Abel ODE, First kind Maple ✓ |
| ODE 79 |
\(y'(x)=y(x)^2 \left (a e^x+y(x)\right )\) Solution method Abel ODE, First kind Maple ✓ |
| ODE 80 |
\(3 a (y(x)+2 x) y(x)^2+y'(x)=0\) Solution method Abel ODE, First kind Maple ✓ |
| ODE 81 |
\(y'(x)=y(x) \left (a+b y(x)^2\right )\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 82 |
\(y'(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2+\text {a3} y(x)^3\) Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 83 |
\(y'(x)=x y(x)^3\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 84 |
\(y'(x)+y(x) \left (1-x y(x)^2\right )=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 85 |
\(y'(x)=y(x)^2 (a+b x y(x))\) Solution method Abel ODE, First kind Maple ✓ |
| ODE 86 |
\(y(x)^3 \left (a+4 b^2 x+3 b x^2\right )+y'(x)+3 x y(x)^2=0\) Solution method Abel ODE, First kind Maple ✓ |
| ODE 87 |
\(y'(x)=y(x)^2 \left (x^3 y(x)+1\right )\) Solution method Abel ODE, First kind Maple ✗ |
| ODE 88 |
\(2 x y(x) \left (a x y(x)^2+1\right )+y'(x)=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 89 |
\(y'(x)=y(x)^2-a x \left (1-x^{n-1}\right ) y(x)^3\) Solution method Abel ODE, First kind Maple ✗ |
| ODE 90 |
\(y'(x)=a y(x)^2+x y(x)^3 \left (b+c x^{n-1}\right )\) Solution method Abel ODE, First kind Maple ✗ |
| ODE 91 |
\(y'(x)+y(x) \left (y(x)^2 \sec (x)+\tan (x)\right )=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 92 |
\(y'(x)+y(x)^3 \tan (x) \sec (x)=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 93 |
\(y'(x)=\text {f0}(x)+\text {f1}(x) y(x)+\text {f2}(x) y(x)^2+\text {f3}(x) y(x)^3\) Solution method Abel ODE, First kind Maple ✗ |
| ODE 94 |
\(y'(x)=y(x) \left (y(x)^3 \sec (x)+\tan (x)\right )\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 95 |
\(y'(x)=a x^{\frac {n}{1-n}}+b y(x)^n\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 96 |
\(y'(x)=f(x) y(x)+g(x) y(x)^k\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 97 |
\(y'(x)=f(x)+g(x) y(x)+h(x) y(x)^n\) Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 98 |
\(y'(x)=f(x) y(x)^m+g(x) y(x)^n\) Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 99 |
\(y'(x)=\sqrt {\left | y(x)\right | }\) Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 100 |
\(y'(x)=a+\sqrt {\text {A0}+\text {B0} y(x)}+b y(x)\) Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 101 |
\(y'(x)=a x+b \sqrt {y(x)}\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 102 |
\(x^3+y'(x)=x \sqrt {x^4+4 y(x)}\) Solution method Homogeneous equation, isobaric equation Maple ✓ |
| ODE 103 |
\(y'(x)+2 \left (1-x \sqrt {y(x)}\right ) y(x)=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 104 |
\(y'(x)=\sqrt {a+b y(x)^2}\) Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 105 |
\(y'(x)=y(x) \sqrt {a+b y(x)}\) Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 106 |
\(g(x) (f(x)-y(x)) \sqrt {(y(x)-a) (y(x)-b)}+y'(x)=0\) Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 107 |
\(y'(x)=\sqrt {X Y}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 108 |
\(y'(x)=\text {R1}\left (x,\sqrt {X}\right ) \text {R2}\left (y(x),\sqrt {Y}\right )\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 109 |
\(y'(x)=\cos ^2(x) \cos (y(x))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 110 |
\(y'(x)=\sec ^2(x) \text {Cosy}(y(x)) \cot (y(x))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 111 |
\(y'(x)=a+b \cos (A x+B y(x))\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 112 |
\(y'(x)=-\left (1-f'(x)\right ) \cos (y(x))+f'(x)-f(x) \sin (y(x))+1\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 113 |
\(g(x) \sin (a y(x))+h(x) \cos (a y(x))+f(x)+y'(x)=0\) Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 114 |
\(y'(x)=a+b \cos (y(x))\) Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 115 |
\(x \left (\sin (2 y(x))-x^2 \cos ^2(y(x))\right )+y'(x)=0\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 116 |
\(y'(x)+\tan (x) \sec (x) \cos ^2(y(x))=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 117 |
\(y'(x)=\cot (x) \cot (y(x))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 118 |
\(y'(x)+\cot (x) \cot (y(x))=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 119 |
\(y'(x)=\sin (x) (\csc (y(x))-\cot (y(x)))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 120 |
\(y'(x)=\tan (x) \cot (y(x))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 121 |
\(y'(x)+\tan (x) \cot (y(x))=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 122 |
\(y'(x)+\sin (2 x) \csc (2 y(x))=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 123 |
\(y'(x)=\tan (x) (\tan (y(x))+\sec (x) \sec (y(x)))\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 124 |
\(y'(x)=\cos (x) \sec ^2(y(x))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 125 |
\(y'(x)=\sec ^2(x) \sec ^3(y(x))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 126 |
\(y'(x)=a+b \sin (y(x))\) Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 127 |
\(y'(x)=a+b \sin (A x+B y(x))\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 128 |
\(y'(x)=\tan (y(x)) (\cos (x) \sin (y(x))+1)\) Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 129 |
\(y'(x)+\csc (2 x) \sin (2 y(x))=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 130 |
\(f(x)+g(x) \tan (y(x))+y'(x)=0\) Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 131 |
\(y'(x)=\sqrt {a+b \cos (y(x))}\) Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 132 |
\(y'(x)=e^{y(x)}+x\) Solution method Series solution to \(y'(x)=f(x,y(x))\), case \(f(x,y)\) analytic Maple ✓ |
| ODE 133 |
\(y'(x)=e^{y(x)+x}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 134 |
\(y'(x)=e^x \left (a+b e^{-y(x)}\right )\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 135 |
\(y'(x)+y(x) \log (x) \log (y(x))=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 136 |
\(y'(x)=x^{m-1} y(x)^{1-n} f\left (a x^m+b y(x)^n\right )\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 137 |
\(y'(x)=a f(y(x))\) Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 138 |
\(y'(x)=f(a+b x+c y(x))\) Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\) Maple ✓ |
| ODE 139 |
\(y'(x)=f(x) g(y(x))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 140 |
\(y'(x)=\text {Csx}(x) y(x) \sec (x)+\sec ^2(x)\) Solution method Linear ODE Maple ✓ |
| ODE 141 |
\(2 y'(x)+2 \csc ^2(x)=y(x) \csc (x) \sec (x)-y(x)^2 \sec ^2(x)\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 142 |
\(2 y'(x)=2 \sin ^2(y(x)) \tan (y(x))-x \sin (2 y(x))\) Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 143 |
\(a x+2 y'(x)=\sqrt {a^2 x^2-4 b x^2-4 c y(x)}\) Solution method Homogeneous equation, isobaric equation Maple ✓ |
| ODE 144 |
\(3 y'(x)=\sqrt {x^2-3 y(x)}+x\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 145 |
\(x y'(x)=\sqrt {a^2-x^2}\) Solution method Separable ODE, Dependent variable missing Maple ✓ |
| ODE 146 |
\(x y'(x)+y(x)+x=0\) Solution method Linear ODE Maple ✓ |
| ODE 147 |
\(x^2+x y'(x)-y(x)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 148 |
\(x y'(x)=x^3-y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 149 |
\(x y'(x)=x^3+y(x)+1\) Solution method Linear ODE Maple ✓ |
| ODE 150 |
\(x y'(x)=x^m+y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 151 |
\(x y'(x)=x \sin (x)-y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 152 |
\(x y'(x)=x^2 \sin (x)+y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 153 |
\(x y'(x)=x^n \log (x)-y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 154 |
\(x y'(x)=\sin (x)-2 y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 155 |
\(x y'(x)=a y(x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 156 |
\(x y'(x)=a y(x)+x+1\) Solution method Linear ODE Maple ✓ |
| ODE 157 |
\(x y'(x)=a x+b y(x)\) Solution method Homogeneous equation Maple ✓ |
| ODE 158 |
\(x y'(x)=a x^2+b y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 159 |
\(x y'(x)=a+b x^n+c y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 160 |
\(x y'(x)+(3-x) y(x)+2=0\) Solution method Linear ODE Maple ✓ |
| ODE 161 |
\((a x+2) y(x)+x y'(x)+x=0\) Solution method Linear ODE Maple ✓ |
| ODE 162 |
\(y(x) (a+b x)+x y'(x)=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 163 |
\(x y'(x)=x^3+\left (1-2 x^2\right ) y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 164 |
\(x y'(x)=a x-\left (1-b x^2\right ) y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 165 |
\(\left (2-a x^2\right ) y(x)+x y'(x)+x=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 166 |
\(x^2+x y'(x)+y(x)^2=0\) Solution method Riccati ODE, Special cases Maple ✓ |
| ODE 167 |
\(x y'(x)=x^2+y(x) (y(x)+1)\) Solution method Riccati ODE, Special cases Maple ✓ |
| ODE 168 |
\(x y'(x)+y(x)^2-y(x)=x^{2/3}\) Solution method Riccati ODE, Special cases Maple ✓ |
| ODE 169 |
\(x y'(x)=a+b y(x)^2\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 170 |
\(x y'(x)=a x^2+b y(x)^2+y(x)\) Solution method Riccati ODE, Special cases Maple ✓ |
| ODE 171 |
\(x y'(x)=a x^{2 n}+y(x) (b y(x)+n)\) Solution method Riccati ODE, Special cases Maple ✓ |
| ODE 172 |
\(x y'(x)=a x^n+b y(x)+c y(x)^2\) Solution method Riccati ODE, Special cases Maple ✓ |
| ODE 173 |
\(x y'(x)=a x^n+b y(x)+c y(x)^2+k\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 174 |
\(a+x y'(x)+x y(x)^2=0\) Solution method Riccati ODE, Main form Maple ✓ |
| ODE 175 |
\(x y'(x)+y(x) (1-x y(x))=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 176 |
\(x y'(x)=y(x) (1-x y(x))\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 177 |
\(x y'(x)=y(x) (x y(x)+1)\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 178 |
\(x y'(x)=a x^3 y(x) (1-x y(x))\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 179 |
\(x y'(x)=x^3+\left (2 x^2+1\right ) y(x)+x y(x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 180 |
\(x y'(x)=y(x) (2 x y(x)+1)\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 181 |
\(y(x) (a x y(x)+2)+b x+x y'(x)=0\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 182 |
\(\text {a0}+\text {a1} x+y(x) (\text {a2}+\text {a3} x y(x))+x y'(x)=0\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 183 |
\(a x^2 y(x)^2+x y'(x)+2 y(x)=b\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 184 |
\(\frac {1}{2} (n-m) y(x)+x^m+x^n y(x)^2+x y'(x)=0\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 185 |
\(y(x) \left (a+b x^n y(x)\right )+x y'(x)=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 186 |
\(x y'(x)=a x^m-b y(x)-c x^n y(x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 187 |
\(x y'(x)=a x^n (x-y(x))^2-y(x)+2 x\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 188 |
\(y(x) (1-a y(x) \log (x))+x y'(x)=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 189 |
\(x y'(x)=f(x) \left (x^2-y(x)^2\right )+y(x)\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 190 |
\(x y'(x)=y(x) \left (y(x)^2+1\right )\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 191 |
\(x y'(x)+y(x) \left (1-x y(x)^2\right )=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 192 |
\(x y'(x)+y(x)=a \left (x^2+1\right ) y(x)^3\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 193 |
\(x y'(x)=a y(x)+b \left (x^2+1\right ) y(x)^3\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 194 |
\(x y'(x)+2 y(x)=a x^{2 k} y(x)^k\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 195 |
\(x y'(x)=4 \left (y(x)-\sqrt {y(x)}\right )\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 196 |
\(x y'(x)+2 y(x)=\sqrt {y(x)^2+1}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 197 |
\(x y'(x)=\sqrt {x^2+y(x)^2}+y(x)\) Solution method Homogeneous equation Maple ✓ |
| ODE 198 |
\(x y'(x)=\sqrt {x^2-y(x)^2}+y(x)\) Solution method Homogeneous equation Maple ✓ |
| ODE 199 |
\(x y'(x)=x \sqrt {x^2+y(x)^2}+y(x)\) Solution method Homogeneous equation, \(xy'(x)=x f(x) g(u)+y(x)\) Maple ✓ |
| ODE 200 |
\(x y'(x)=y(x)-x (x-y(x)) \sqrt {x^2+y(x)^2}\) Solution method Homogeneous equation, \(xy'(x)=x f(x) g(u)+y(x)\) Maple ✓ |
| ODE 201 |
\(x y'(x)=a \sqrt {b^2 x^2+y(x)^2}+y(x)\) Solution method Homogeneous equation Maple ✓ |
| ODE 202 |
\(\cos (y(x)) \left (\sin (y(x))-3 x^2 \cos (y(x))\right )+x y'(x)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 203 |
\(x y'(x)-y(x)+x \cos \left (\frac {y(x)}{x}\right )+x=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 204 |
\(x y'(x)=y(x)-x \cos ^2\left (\frac {y(x)}{x}\right )\) Solution method Homogeneous equation Maple ✓ |
| ODE 205 |
\(x y'(x)=\left (1-2 x^2\right ) \cot ^2(y(x))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 206 |
\(x y'(x)=y(x)-\cot ^2(y(x))\) Solution method Homogeneous equation Maple ✓ |
| ODE 207 |
\(x y'(x)+y(x)+2 x \sec (x y(x))=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 208 |
\(x y'(x)-y(x)+x \sec \left (\frac {y(x)}{x}\right )=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 209 |
\(x y'(x)=y(x)+x \sec ^2\left (\frac {y(x)}{x}\right )\) Solution method Homogeneous equation Maple ✓ |
| ODE 210 |
\(x y'(x)=\sin (x-y(x))\) Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 211 |
\(x y'(x)=y(x)+x \sin \left (\frac {y(x)}{x}\right )\) Solution method Homogeneous equation Maple ✓ |
| ODE 212 |
\(x y'(x)+\tan (y(x))=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 213 |
\(x y'(x)+\tan (y(x)+x)+x=0\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 214 |
\(x y'(x)=y(x)-x \tan \left (\frac {y(x)}{x}\right )\) Solution method Homogeneous equation Maple ✓ |
| ODE 215 |
\(x y'(x)=\left (y(x)^2+1\right ) \left (x^2+\tan ^{-1}(y(x))\right )\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 216 |
\(x y'(x)=x e^{\frac {y(x)}{x}}+y(x)\) Solution method Homogeneous equation Maple ✓ |
| ODE 217 |
\(x y'(x)=x e^{\frac {y(x)}{x}}+y(x)+x\) Solution method Homogeneous equation Maple ✓ |
| ODE 218 |
\(x y'(x)=y(x) \log (y(x))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 219 |
\(x y'(x)=y(x) (-\log (y(x))+\log (x)+1)\) Solution method Homogeneous equation Maple ✓ |
| ODE 220 |
\(x y'(x)+y(x) (-\log (y(x))-\log (x)+1)=0\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 221 |
\(x y'(x)=y(x)-2 x \tanh \left (\frac {y(x)}{x}\right )\) Solution method Homogeneous equation Maple ✓ |
| ODE 222 |
\(n y(x)+x y'(x)=f(x) g\left (x^n y(x)\right )\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 223 |
\(x y'(x)=y(x) f\left (x^m y(x)^n\right )\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 224 |
\((x+1) y'(x)=(3 x+4) x^3+y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 225 |
\((x+1) y'(x)=2 y(x)+(x+1)^4\) Solution method Linear ODE Maple ✓ |
| ODE 226 |
\((x+1) y'(x)=n y(x)+e^x (x+1)^{n+1}\) Solution method Linear ODE Maple ✓ |
| ODE 227 |
\((x+1) y'(x)=a y(x)+b x y(x)^2\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 228 |
\((x+1) y'(x)+(x+1)^4 y(x)^3+y(x)=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 229 |
\((x+1) y'(x)=y(x) \left (1-x y(x)^3\right )\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 230 |
\((x+1) y'(x)=(x+1) \sqrt {y(x)+1}+y(x)+1\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 231 |
\((a+x) y'(x)=b x\) Solution method Separable ODE, Dependent variable missing Maple ✓ |
| ODE 232 |
\((a+x) y'(x)=b x+y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 233 |
\((a+x) y'(x)+b x^2+y(x)=0\) Solution method Linear ODE Maple ✓ |
| ODE 234 |
\((a+x) y'(x)=2 (a+x)^5+3 y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 235 |
\((a+x) y'(x)=b+c y(x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 236 |
\((a+x) y'(x)=b x+c y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 237 |
\((a+x) y'(x)=y(x) (1-a y(x))\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 238 |
\((a-x) y'(x)=y(x)^3 (b+c x)+y(x)\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 239 |
\(2 x y'(x)=2 x^3-y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 240 |
\(2 x y'(x)+1=y(x)^2+4 i x y(x)\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 241 |
\(2 x y'(x)=y(x) \left (y(x)^2+1\right )\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 242 |
\(2 x y'(x)+y(x) \left (y(x)^2+1\right )=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 243 |
\(2 x y'(x)=y(x) \left (-6 y(x)^2+x+1\right )\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 244 |
\(\sqrt {a^2-4 b-4 c y(x)}+a+2 x y'(x)+4 y(x)=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 245 |
\((1-2 x) y'(x)=2 (-3 y(x)+16 x+8)\) Solution method Linear ODE Maple ✓ |
| ODE 246 |
\((2 x+1) y'(x)=4 e^{-y(x)}-2\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 247 |
\(2 (1-x) y'(x)=y(x)+4 \sqrt {1-x} x\) Solution method Linear ODE Maple ✓ |
| ODE 248 |
\(2 (x+1) y'(x)+(x+1)^4 y(x)^3+2 y(x)=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 249 |
\(3 x y'(x)=3 x^{2/3}+(1-3 y(x)) y(x)\) Solution method Riccati ODE, Special cases Maple ✓ |
| ODE 250 |
\(3 x y'(x)=y(x) \left (x y(x)^3+2\right )\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 251 |
\(3 x y'(x)=y(x) \left (3 x y(x)^3 \log (x)+1\right )\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 252 |
\(x^2 y'(x)=a-y(x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 253 |
\(x^2 y'(x)=a+b x+c x^2+x y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 254 |
\(x^2 y'(x)=a+b x+c x^2-x y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 255 |
\(x^2 y'(x)+(1-2 x) y(x)=x^2\) Solution method Linear ODE Maple ✓ |
| ODE 256 |
\(x^2 y'(x)=a+b x y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 257 |
\(x^2 y'(x)=y(x) (a+b x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 258 |
\(x^2 y'(x)+(x+2) x y(x)=\left (1-e^{-2 x}\right ) x-2\) Solution method Linear ODE Maple ✓ |
| ODE 259 |
\(x^2 y'(x)+2 (1-x) x y(x)=e^x \left (2 e^x-1\right )\) Solution method Linear ODE Maple ✓ |
| ODE 260 |
\(x^2 y'(x)+x^2+x y(x)+y(x)^2=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 261 |
\(x^2 y'(x)=(-y(x)+2 x+1)^2\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 262 |
\(x^2 y'(x)=a+b y(x)^2\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 263 |
\(x^2 y'(x)=y(x) (a y(x)+x)\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 264 |
\(x^2 y'(x)=y(x) (a x+b y(x))\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 265 |
\(a x^2+b x y(x)+c y(x)^2+x^2 y'(x)=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 266 |
\(x^2 y'(x)=a+b x^n+x^2 y(x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 267 |
\(x^2 y'(x)+x y(x) (x y(x)+4)+2=0\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 268 |
\(a x (1-x y(x))+x^2 y'(x)+x^2 \left (-y(x)^2\right )+2=0\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 269 |
\(x^2 y'(x)=a+b x^2 y(x)^2\) Solution method Riccati ODE, Main form Maple ✓ |
| ODE 270 |
\(x^2 y'(x)=a+b x^n+c x^2 y(x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 271 |
\(x^2 y'(x)=a+b x y(x)+c x^2 y(x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 272 |
\(x^2 y'(x)=a+b x y(x)+c x^4 y(x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 273 |
\(x^2 y'(x)+y(x) \left (x^2+y(x)^2-x\right )=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 274 |
\(x^2 y'(x)=2 y(x) \left (x-y(x)^2\right )\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 275 |
\(x^2 y'(x)=a x^2 y(x)^2-a y(x)^3\) Solution method Abel ODE, Second kind Maple ✓ |
| ODE 276 |
\(a y(x)^2+b x^2 y(x)^3+x^2 y'(x)=0\) Solution method Abel ODE, Second kind Maple ✓ |
| ODE 277 |
\(x^2 y'(x)=y(x) \left (a x+b y(x)^3\right )\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 278 |
\(x^2 y'(x)+x y(x)+\sqrt {y(x)}=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 279 |
\(x^2 y'(x)=3 x \tan (y(x))+\sec (y(x))\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 280 |
\(\left (1-x^2\right ) y'(x)=-x^2+y(x)+1\) Solution method Linear ODE Maple ✓ |
| ODE 281 |
\(\left (1-x^2\right ) y'(x)+1=x y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 282 |
\(\left (1-x^2\right ) y'(x)=5-x y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 283 |
\(a+\left (x^2+1\right ) y'(x)+x y(x)=0\) Solution method Linear ODE Maple ✓ |
| ODE 284 |
\(a+\left (x^2+1\right ) y'(x)-x y(x)=0\) Solution method Linear ODE Maple ✓ |
| ODE 285 |
\(a+\left (1-x^2\right ) y'(x)-x y(x)=0\) Solution method Linear ODE Maple ✓ |
| ODE 286 |
\(\left (1-x^2\right ) y'(x)+x y(x)-x=0\) Solution method Linear ODE Maple ✓ |
| ODE 287 |
\(\left (1-x^2\right ) y'(x)-x^2+x y(x)=0\) Solution method Linear ODE Maple ✓ |
| ODE 288 |
\(\left (1-x^2\right ) y'(x)+x^2+x y(x)=0\) Solution method Linear ODE Maple ✓ |
| ODE 289 |
\(\left (x^2+1\right ) y'(x)=x \left (x^2+1\right )-x y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 290 |
\(\left (x^2+1\right ) y'(x)=x \left (3 x^2-y(x)\right )\) Solution method Linear ODE Maple ✓ |
| ODE 291 |
\(\left (1-x^2\right ) y'(x)+2 x y(x)=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 292 |
\(\left (x^2+1\right ) y'(x)=2 x (x-y(x))\) Solution method Linear ODE Maple ✓ |
| ODE 293 |
\(\left (x^2+1\right ) y'(x)=2 x \left (x^2+1\right )^2+2 x y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 294 |
\(\left (1-x^2\right ) y'(x)+\cos (x)=2 x y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 295 |
\(\left (x^2+1\right ) y'(x)=\tan (x)-2 x y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 296 |
\(\left (1-x^2\right ) y'(x)=a+4 x y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 297 |
\(\left (x^2+1\right ) y'(x)=y(x) (a+2 b x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 298 |
\(\left (x^2+1\right ) y'(x)=y(x)^2+1\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 299 |
\(\left (1-x^2\right ) y'(x)=1-y(x)^2\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 300 |
\(\left (1-x^2\right ) y'(x)=1-(2 x-y(x)) y(x)\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 301 |
\(\left (1-x^2\right ) y'(x)=n \left (y(x)^2-2 x y(x)+1\right )\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 302 |
\(\left (x^2+1\right ) y'(x)+x (1-y(x)) y(x)=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 303 |
\(\left (1-x^2\right ) y'(x)=x y(x) (a y(x)+1)\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 304 |
\(\left (x^2+1\right ) y'(x)=y(x)^2-2 x \left (y(x)^2+1\right ) y(x)+1\) Solution method Abel ODE, Second kind Maple ✓ |
| ODE 305 |
\(\left (x^2+1\right ) y'(x)+x \sin (y(x)) \cos (y(x))=x \left (x^2+1\right ) \cos ^2(y(x))\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 306 |
\(\left (x^2+1\right ) y'(x)=x^2-y(x) \cot ^{-1}(x)+1\) Solution method Linear ODE Maple ✓ |
| ODE 307 |
\(\left (4-x^2\right ) y'(x)+4 y(x)=(x+2) y(x)^2\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 308 |
\(\left (a^2+x^2\right ) y'(x)=b+x y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 309 |
\(\left (a^2+x^2\right ) y'(x)=\left (\sqrt {a^2+x^2}+x\right ) (b+y(x))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 310 |
\(\left (a^2+x^2\right ) y'(x)+(x-y(x)) y(x)=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 311 |
\(\left (a^2+x^2\right ) y'(x)=a^2-2 y(x)^2+3 x y(x)\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 312 |
\(\left (a^2+x^2\right ) y'(x)+b x y(x)^2+x y(x)=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 313 |
\((1-x) x y'(x)=a+(x+1) y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 314 |
\((1-x) x y'(x)=2 (x y(x)+1)\) Solution method Linear ODE Maple ✓ |
| ODE 315 |
\((1-x) x y'(x)=2 (x y(x)-1)\) Solution method Linear ODE Maple ✓ |
| ODE 316 |
\(x (x+1) y'(x)=(1-2 x) y(x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 317 |
\((1-x) x y'(x)+(2 x+1) y(x)=a\) Solution method Linear ODE Maple ✓ |
| ODE 318 |
\((1-x) x y'(x)=a+2 (2-x) y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 319 |
\((1-x) x y'(x)-3 x y(x)+y(x)+2=0\) Solution method Linear ODE Maple ✓ |
| ODE 320 |
\(x (x+1) y'(x)=\left (x^2+x-1\right ) y(x)+(x+1) \left (x^2-1\right )\) Solution method Linear ODE Maple ✓ |
| ODE 321 |
\(x^2+(x-3) (x-2) y'(x)+3 x y(x)-8 y(x)=0\) Solution method Linear ODE Maple ✓ |
| ODE 322 |
\(x (a+x) y'(x)=y(x) (b+c y(x))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 323 |
\((a+x)^2 y'(x)=2 (a+x) (b+y(x))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 324 |
\(k (-a+y(x)+x)^2+(x-a)^2 y'(x)+y(x)^2=0\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 325 |
\((x-a) (x-b) y'(x)+k y(x)=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 326 |
\((x-a) (x-b) y'(x)=y(x) (-a-b+2 x)+(x-a) (x-b)\) Solution method Linear ODE Maple ✓ |
| ODE 327 |
\((x-a) (x-b) y'(x)=c y(x)^2\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 328 |
\(k (y(x)-a) (y(x)-b)+(x-a) (x-b) y'(x)=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 329 |
\(k (-a+y(x)+x) (-b+y(x)+x)+(x-a) (x-b) y'(x)+y(x)^2=0\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 330 |
\(2 x^2 y'(x)=y(x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 331 |
\(2 x^2 y'(x)+2 x^2 y(x) \cot (x)+x \cot (x)-1=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 332 |
\(2 x^2 y'(x)+x^2 \left (-y(x)^2\right )+2 x y(x)+1=0\) Solution method Homogeneous equation, isobaric equation Maple ✓ |
| ODE 333 |
\(2 x^2 y'(x)=\left (x^2-y(x)^2\right ) (1-x \cot (x))+2 x y(x)\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 334 |
\(2 \left (1-x^2\right ) y'(x)=\sqrt {1-x^2}+(x+1) y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 335 |
\((1-2 x) x y'(x)+(1-4 x) y(x)+1=0\) Solution method Linear ODE Maple ✓ |
| ODE 336 |
\((1-2 x) x y'(x)=y(x)^2-(4 x+1) y(x)+4 x\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 337 |
\(2 (1-x) x y'(x)+(1-2 x) y(x)+x=0\) Solution method Linear ODE Maple ✓ |
| ODE 338 |
\(2 (1-x) x y'(x)+(1-x) y(x)^2+x=0\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 339 |
\(2 \left (x^2+x+1\right ) y'(x)=8 x^2-(2 x+1) y(x)+1\) Solution method Linear ODE Maple ✓ |
| ODE 340 |
\(4 \left (x^2+1\right ) y'(x)-x^2-4 x y(x)=0\) Solution method Linear ODE Maple ✓ |
| ODE 341 |
\(a x^2 y'(x)=a x y(x)+b^2 y(x)^2+x^2\) Solution method Homogeneous equation Maple ✓ |
| ODE 342 |
\(\left (a+b x^2\right ) y'(x)=A+B y(x)^2\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 343 |
\(\left (a+b x^2\right ) y'(x)=c x y(x) \log (y(x))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 344 |
\(x (a x+1) y'(x)+a-y(x)=0\) Solution method Linear ODE Maple ✓ |
| ODE 345 |
\((a+b x)^2 y'(x)+y(x)^3 (a+b x)+c y(x)^2=0\) Solution method Abel ODE, Second kind Maple ✓ |
| ODE 346 |
\(x^3 y'(x)=a+b x^2 y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 347 |
\(x^3 y'(x)=x^2 y(x)-x^2+3\) Solution method Linear ODE Maple ✓ |
| ODE 348 |
\(x^3 y'(x)=x^4+y(x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 349 |
\(x^3 y'(x)=y(x) \left (x^2+y(x)\right )\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 350 |
\(x^3 y'(x)=x^2 (y(x)-1)+y(x)^2\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 351 |
\(x^3 y'(x)=(x+1) y(x)^2\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 352 |
\(x^3 y'(x)+x^2 y(x) \left (1-x^2 y(x)\right )+20=0\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 353 |
\(x^6 \left (-y(x)^2\right )+x^3 y'(x)+(3-2 x) x^2 y(x)+3=0\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 354 |
\(x^3 y'(x)=y(x) \left (2 x^2+y(x)^2\right )\) Solution method Homogeneous equation Maple ✓ |
| ODE 355 |
\(x^3 y'(x)=\cos (y(x)) \left (\cos (y(x))-2 x^2 \sin (y(x))\right )\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 356 |
\(x \left (x^2+1\right ) y'(x)=a x^2+y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 357 |
\(x \left (1-x^2\right ) y'(x)=a x^2+y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 358 |
\(x \left (x^2+1\right ) y'(x)=a x^3+y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 359 |
\(x \left (x^2+1\right ) y'(x)=a-x^2 y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 360 |
\(x \left (x^2+1\right ) y'(x)=\left (1-x^2\right ) y(x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 361 |
\(x \left (1-x^2\right ) y'(x)=\left (x^2-x+1\right ) y(x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 362 |
\(x \left (1-x^2\right ) y'(x)=a x^3+\left (1-2 x^2\right ) y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 363 |
\(x \left (1-x^2\right ) y'(x)=\left (1-2 x^2\right ) y(x)+\left (1-x^2\right ) x^3\) Solution method Linear ODE Maple ✓ |
| ODE 364 |
\(x \left (x^2+1\right ) y'(x)=2 \left (1-2 x^2 y(x)\right )\) Solution method Linear ODE Maple ✓ |
| ODE 365 |
\(x \left (x^2+1\right ) y'(x)=x-\left (5 x^2+3\right ) y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 366 |
\(\left (1-x^2\right ) x y'(x)+\left (1-x^2\right ) y(x)^2+x^2=0\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 367 |
\((1-x) x^2 y'(x)=(2-x) x y(x)-y(x)^2\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 368 |
\(2 x^3 y'(x)=y(x) \left (x^2-y(x)^2\right )\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 369 |
\(2 x^3 y'(x)=y(x) \left (a y(x)^2+3 x^2\right )\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 370 |
\(6 x^3 y'(x)=4 x^2 y(x)+(1-3 x) y(x)^4\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 371 |
\(x y'(x) \left (a+b x+c x^2\right )-y(x) \left (a+b x+c x^2\right )+x^2=y(x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 372 |
\(x^4 y'(x)=y(x) \left (x^3+y(x)\right )\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 373 |
\(a^2+x^4 y'(x)+x^4 y(x)^2=0\) Solution method Riccati ODE, Main form Maple ✓ |
| ODE 374 |
\(x^4 y'(x)+x^3 y(x)+\csc (x y(x))=0\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 375 |
\(\left (1-x^4\right ) y'(x)=2 x \left (1-y(x)^2\right )\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 376 |
\(x \left (1-x^3\right ) y'(x)=2 x-\left (1-4 x^3\right ) y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 377 |
\(x \left (1-x^3\right ) y'(x)=x^2+y(x) (1-2 x y(x))\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 378 |
\(x^2 \left (1-x^2\right ) y'(x)=y(x) \left (x-3 x^3 y(x)\right )\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 379 |
\(x \left (1-2 x^3\right ) y'(x)=2 \left (1-x^3\right ) y(x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 380 |
\(\left (y'(x)+y(x)^2\right ) \left (a+b x+c x^2\right )^2+A=0\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 381 |
\(x^5 y'(x)=1-3 x^4 y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 382 |
\(x \left (1-x^4\right ) y'(x)=\left (1-x^4\right ) y(x)+2 x \left (x^2-y(x)^2\right )\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 383 |
\(x^7 y'(x)+5 x^3 y(x)^2+2 \left (x^2+1\right ) y(x)^3=0\) Solution method Abel ODE, First kind Maple ✓ |
| ODE 384 |
\(x^n y'(x)=a+b x^{n-1} y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 385 |
\(x^n y'(x)=x^{2 n-1}-y(x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 386 |
\(y(x) \left (x^{n-1}+y(x)\right )+x^n y'(x)+x^2=0\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 387 |
\((1-n) x^{n-1}+x^{2 n-2}+x^n y'(x)+y(x)^2=0\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 388 |
\(x^n y'(x)=a^2 x^{2 n-2}+b^2 y(x)^2\) Solution method Riccati ODE, Generalized ODE Maple ✓ |
| ODE 389 |
\(x^n y'(x)=x^{n-1} \left (a x^{2 n}-b y(x)^2+n y(x)\right )\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 390 |
\(x^{2 n} y'(x)=-n x^{n-1}+x^n y(x) \left (x^{2 n} y(x)^2-3 x^n y(x)+1\right )+1\) Solution method Abel ODE, First kind Maple ✓ |
| ODE 391 |
\(x^k y'(x)=a x^m+b y(x)^n\) Solution method Change of Variable, new dependent variable Maple ✗ |
| ODE 392 |
\(\sqrt {x^2+1} y'(x)=2 x-y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 393 |
\(\sqrt {1-x^2} y'(x)=y(x)^2+1\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 394 |
\(\left (x-\sqrt {x^2+1}\right ) y'(x)=y(x)+\sqrt {y(x)^2+1}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 395 |
\(\sqrt {a^2+x^2} y'(x)+y(x)+x=\sqrt {a^2+x^2}\) Solution method Linear ODE Maple ✓ |
| ODE 396 |
\(\sqrt {b^2+x^2} y'(x)=\sqrt {a^2+y(x)^2}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 397 |
\(\sqrt {b^2-x^2} y'(x)=\sqrt {a^2-y(x)^2}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 398 |
\(x \sqrt {a^2+x^2} y'(x)=y(x) \sqrt {b^2+y(x)^2}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 399 |
\(x \sqrt {x^2-a^2} y'(x)=y(x) \sqrt {y(x)^2-b^2}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 400 |
\(\sqrt {X} y'(x)+\sqrt {Y}=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 401 |
\(\sqrt {X} y'(x)=\sqrt {Y}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 402 |
\(x^{3/2} y'(x)=a+b x^{3/2} y(x)^2\) Solution method Abel ODE, First kind Maple ✓ |
| ODE 403 |
\(\sqrt {x^3+1} y'(x)=\sqrt {y(x)^3+1}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 404 |
\(\sqrt {(1-x) x (1-a x)} y'(x)=\sqrt {(1-y(x)) y(x) (1-a y(x))}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 405 |
\(\sqrt {1-x^4} y'(x)=\sqrt {1-y(x)^4}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 406 |
\(\sqrt {x^4+x^2+1} y'(x)=\sqrt {y(x)^4+y(x)^2+1}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 407 |
\(\sqrt {X} y'(x)=0\) Solution method Separable ODE, Dependent variable missing Maple ✓ |
| ODE 408 |
\(\sqrt {X} y'(x)+\sqrt {Y}=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 409 |
\(\sqrt {X} y'(x)=\sqrt {Y}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 410 |
\(\left (x^3+1\right )^{2/3} y'(x)+\left (y(x)^3+1\right )^{2/3}=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 411 |
\(\left (\text {a0}+\text {a1} x+4 x^3\right )^{2/3} y'(x)+\left (\text {a0}+\text {a1} y(x)+4 y(x)^3\right )^{2/3}=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 412 |
\(X^{2/3} y'(x)=Y^{2/3}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 413 |
\(\left (a+\cos ^2\left (\frac {x}{2}\right )\right ) y'(x)=y(x) \tan \left (\frac {x}{2}\right ) \left (a-y(x)+\cos ^2\left (\frac {x}{2}\right )+1\right )\) Solution method Change of Variable, Two new variables Maple ✓ |
| ODE 414 |
\(\left (1-4 \cos ^2(x)\right ) y'(x)=y(x) \left (4 \cos ^2(x)+1\right ) \tan (x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 415 |
\((1-\sin (x)) y'(x)+y(x) \cos (x)=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 416 |
\(y'(x) (\cos (x)-\sin (x))+y(x) (\sin (x)+\cos (x))=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 417 |
\(y'(x) \left (\text {a0}+\text {a1} \sin ^2(x)\right )+\text {a2} x \left (\text {a1} \sin ^2(x)+\text {a3}\right )+\text {a1} y(x) \sin (2 x)=0\) Solution method Linear ODE Maple ✓ |
| ODE 418 |
\(\left (x-e^x\right ) y'(x)+\left (1-e^x\right ) y(x)+e^x x=0\) Solution method Linear ODE Maple ✓ |
| ODE 419 |
\(x \log (x) y'(x)=a x (\log (x)+1)-y(x)\) Solution method Linear ODE Maple ✓ |
| ODE 420 |
\(y(x) y'(x)+x=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 421 |
\(e^{x^2} x+y(x) y'(x)=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 422 |
\(x^3+y(x) y'(x)+y(x)=0\) Solution method Abel ODE, Second kind Maple ✗ |
| ODE 423 |
\(a x+b y(x)+y(x) y'(x)=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 424 |
\(y(x) y'(x)+e^{-x} x (y(x)+1)=0\) Solution method Linear ODE Maple ✓ |
| ODE 425 |
\(f(x)+y(x) y'(x)=g(x) y(x)\) Solution method Exact equation, integrating factor Maple ✗ |
| ODE 426 |
\(y(x) y'(x)+y(x)^2+4 x (x+1)=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 427 |
\(y(x) y'(x)=a x+b y(x)^2\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 428 |
\(y(x) y'(x)=a y(x)^2+b \cos (c+x)\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 429 |
\(y(x) y'(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2\) Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 430 |
\(y(x) y'(x)=a x+b x y(x)^2\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 431 |
\(y(x) y'(x)=\csc ^2(x)-y(x)^2 \cot (x)\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 432 |
\(y(x) y'(x)=\sqrt {a^2+y(x)^2}\) Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 433 |
\(y(x) y'(x)=\sqrt {y(x)^2-a^2}\) Solution method Separable ODE, Independent variable missing Maple ✓ |
| ODE 434 |
\(g(x) f\left (x^2+y(x)^2\right )+y(x) y'(x)+x=0\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 435 |
\((y(x)+1) y'(x)=y(x)+x\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 436 |
\((y(x)+1) y'(x)=x^2 (1-y(x))\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 437 |
\((y(x)+x) y'(x)+y(x)=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 438 |
\((x-y(x)) y'(x)=y(x)\) Solution method Homogeneous equation Maple ✓ |
| ODE 439 |
\((y(x)+x) y'(x)-y(x)+x=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 440 |
\((y(x)+x) y'(x)=x-y(x)\) Solution method Homogeneous equation Maple ✓ |
| ODE 441 |
\(1-y'(x)=y(x)+x\) Solution method Homogeneous equation Maple ✓ |
| ODE 442 |
\((x-y(x)) y'(x)=y(x) (2 x y(x)+1)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 443 |
\((y(x)+x) y'(x)+\tan (y(x))=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 444 |
\((x-y(x)) y'(x)=\left (e^{-\frac {x}{y(x)}}+1\right ) y(x)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 445 |
\((y(x)+x+1) y'(x)+3 y(x)+4 x+1=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 446 |
\((y(x)+x+2) y'(x)=-y(x)-x+1\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 447 |
\((-y(x)-x+3) y'(x)=-3 y(x)+x+1\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 448 |
\((y(x)-x+3) y'(x)=3 y(x)-4 x+11\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 449 |
\((y(x)+2 x) y'(x)-2 y(x)+x=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 450 |
\((-y(x)+2 x+2) y'(x)+3 (-y(x)+2 x+1)=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 451 |
\((-y(x)+2 x+3) y'(x)+2=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 452 |
\((-y(x)+2 x+4) y'(x)-2 y(x)+x+5=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 453 |
\((-y(x)-2 x+5) y'(x)-2 y(x)-x+4=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 454 |
\((y(x)-3 x+1) y'(x)=2 (x-y(x))\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 455 |
\((y(x)-3 x+2) y'(x)-3 y(x)-2 x+5=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 456 |
\((4 x-y(x)) y'(x)-5 y(x)+2 x=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 457 |
\((-y(x)-4 x+6) y'(x)=2 x-y(x)\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 458 |
\((-y(x)+5 x+1) y'(x)-5 y(x)+x+5=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 459 |
\(y'(x) (a+b x+y(x))+a-b x-y(x)=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 460 |
\(\left (x^2-y(x)\right ) y'(x)+x=0\) Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 461 |
\(\left (x^2-y(x)\right ) y'(x)=4 x y(x)\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 462 |
\(y'(x) (y(x)-\cot (x) \csc (x))+y(x) \csc (x) (y(x) \cos (x)+1)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 463 |
\(x^2+2 y(x) y'(x)+y(x)^2+2 x=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 464 |
\(2 y(x) y'(x)=x^3+x y(x)^2\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 465 |
\((x-2 y(x)) y'(x)=y(x)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 466 |
\((2 y(x)+x) y'(x)-y(x)+2 x=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 467 |
\((x-2 y(x)) y'(x)+y(x)+2 x=0\) Solution method Exact equation Maple ✓ |
| ODE 468 |
\((-2 y(x)+x+1) y'(x)=-y(x)+2 x+1\) Solution method Exact equation Maple ✓ |
| ODE 469 |
\((2 y(x)+x+1) y'(x)-2 y(x)-x+1=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 470 |
\((2 y(x)+x+1) y'(x)-4 y(x)+x+7=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 471 |
\(x^2+2 (y(x)+x) y'(x)+2 y(x)=0\) Solution method Exact equation Maple ✓ |
| ODE 472 |
\((-2 y(x)+2 x+3) y'(x)=-2 y(x)+6 x+1\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 473 |
\((-2 y(x)-4 x+1) y'(x)+y(x)+2 x=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 474 |
\((6 x-2 y(x)) y'(x)=-y(x)+3 x+2\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 475 |
\((2 y(x)+9 x+19) y'(x)-6 y(x)-2 x+18=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 476 |
\(\left (x^3+2 y(x)\right ) y'(x)=3 x (2-x y(x))\) Solution method Exact equation Maple ✓ |
| ODE 477 |
\(y'(x) (\tan (x) \sec (x)-2 y(x))+\sec (x) (2 y(x) \sin (x)+1)=0\) Solution method Exact equation, integrating factor Maple ✗ |
| ODE 478 |
\(\left (e^{-x} x-2 y(x)\right ) y'(x)=2 e^{-2 x} x-\left (-2 y(x)+e^{-x} x+e^{-x}\right ) y(x)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 479 |
\(3 y(x) y'(x)+5 \cot (x) \cos ^2(y(x)) \cot (y(x))=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 480 |
\(3 (2-y(x)) y'(x)+x y(x)=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 481 |
\((x-3 y(x)) y'(x)-y(x)+3 x+4=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 482 |
\((-3 y(x)-x+4) y'(x)-3 y(x)-x+3=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 483 |
\((3 y(x)+2 x+2) y'(x)=-3 y(x)-2 x+1\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 484 |
\((-3 y(x)-2 x+5) y'(x)-3 y(x)-2 x+1=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 485 |
\((-3 y(x)+9 x+1) y'(x)-y(x)+3 x+2=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 486 |
\((4 y(x)+x) y'(x)-y(x)+4 x=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 487 |
\((4 y(x)+2 x+3) y'(x)=2 y(x)+x+1\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 488 |
\((-4 y(x)+2 x+5) y'(x)=-2 y(x)+x+3\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 489 |
\((-4 y(x)+3 x+5) y'(x)=-3 y(x)+7 x+2\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 490 |
\(4 (-y(x)-x+1) y'(x)-x+2=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 491 |
\((-4 y(x)-11 x+11) y'(x)=-25 y(x)-8 x+62\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 492 |
\((5 y(x)+3 x+6) y'(x)=7 y(x)+x+2\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 493 |
\((5 y(x)+7 x) y'(x)+8 y(x)+10 x=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 494 |
\(\left (4 x^3+5 y(x)+x\right ) y'(x)+7 x^3+3 x^2 y(x)+4 y(x)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 495 |
\((6 y(x)-x+5) y'(x)=4 y(x)-x+3\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 496 |
\(3 (2 y(x)+x) y'(x)=-2 y(x)-x+1\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 497 |
\((7 y(x)-3 x+3) y'(x)+3 y(x)-7 x+7=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 498 |
\((9 y(x)+x+1) y'(x)+5 y(x)+x+1=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 499 |
\((-12 y(x)+5 x+8) y'(x)=-5 y(x)+2 x+3\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 500 |
\((-16 y(x)+7 x+140) y'(x)+y(x)+8 x+25=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 501 |
\((21 y(x)+9 x+3) y'(x)=-5 y(x)+7 x+45\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 502 |
\(y'(x) (a x+b y(x))+x=0\) Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 503 |
\(y'(x) (a x+b y(x))+y(x)=0\) Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 504 |
\(y'(x) (a x+b y(x))+a y(x)+b x=0\) Solution method Exact equation Maple ✓ |
| ODE 505 |
\(y'(x) (a x+b y(x))=a y(x)+b x\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 506 |
\(\text {a1}+y'(x) (\text {a2}+b x+\text {c2} y(x))+b y(x)+\text {b1} x=0\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 507 |
\(y'(x) (\text {a2}+\text {b2} y(x)+\text {c2} y(x))=\text {a1}+\text {b1} x+\text {c1} y(x)\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 508 |
\(x y(x) y'(x)+y(x)^2+1=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 509 |
\(x y(x) y'(x)=y(x)^2+x\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 510 |
\(x^2+x y(x) y'(x)+y(x)^2=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 511 |
\(x^4+x y(x) y'(x)-y(x)^2=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 512 |
\(x y(x) y'(x)=a x^3 \cos (x)+y(x)^2\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 513 |
\(x y(x) y'(x)=x^2-x y(x)+y(x)^2\) Solution method Homogeneous equation Maple ✓ |
| ODE 514 |
\(2 x^2+x y(x) y'(x)-2 x y(x)-y(x)^2=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 515 |
\(x y(x) y'(x)=a+b y(x)^2\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 516 |
\(x y(x) y'(x)=a x^n+b y(x)^2\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 517 |
\(x y(x) y'(x)=\left (x^2+1\right ) \left (1-y(x)^2\right )\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 518 |
\(x^2 \cot ^{-1}\left (\frac {y(x)}{x}\right )+x y(x) y'(x)-y(x)^2=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 519 |
\(x^2 e^{-\frac {2 y(x)}{x}}+x y(x) y'(x)-y(x)^2=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 520 |
\((x y(x)+1) y'(x)+y(x)^2=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 521 |
\(x (y(x)+1) y'(x)-(1-x) y(x)=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 522 |
\(x (1-y(x)) y'(x)+(x+1) y(x)=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 523 |
\(x (1-y(x)) y'(x)+(1-x) y(x)=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 524 |
\(a x+x (y(x)+2) y'(x)=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 525 |
\((x (-y(x))+3 x+2) y'(x)+y(x)=0\) Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 526 |
\(x (y(x)+4) y'(x)=y(x)^2+2 y(x)+2 x\) Solution method Homogeneous equation, special Maple ✓ |
| ODE 527 |
\(x (a+y(x)) y'(x)+b x+c y(x)=0\) Solution method Change of Variable, new independent variable Maple ✗ |
| ODE 528 |
\(x (a+y(x)) y'(x)=y(x) (A+B x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 529 |
\(x (y(x)+x) y'(x)+y(x)^2=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 530 |
\(x (x-y(x)) y'(x)+y(x)^2=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 531 |
\(x (y(x)+x) y'(x)=x^2+y(x)^2\) Solution method Homogeneous equation Maple ✓ |
| ODE 532 |
\(2 x^2+x (x-y(x)) y'(x)+3 x y(x)-y(x)^2=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 533 |
\(x \sqrt {x^2-y(x)^2}+x (y(x)+x) y'(x)-y(x) (y(x)+x)=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 534 |
\((a+x (y(x)+x)) y'(x)=b y(x) (y(x)+x)\) Solution method Homogeneous equation, special Maple ✗ |
| ODE 535 |
\(x (y(x)+2 x) y'(x)=x^2+x y(x)-y(x)^2\) Solution method Homogeneous equation Maple ✓ |
| ODE 536 |
\(4 x^2+x (4 x-y(x)) y'(x)-6 x y(x)-y(x)^2=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 537 |
\(x \left (x^3+y(x)\right ) y'(x)=\left (x^3-y(x)\right ) y(x)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 538 |
\(x \left (2 x^3+y(x)\right ) y'(x)=\left (2 x^3-y(x)\right ) y(x)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 539 |
\(x \left (2 x^3+y(x)\right ) y'(x)=6 y(x)^2\) Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 540 |
\((1-x) y(x) y'(x)+x (1-y(x))=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 541 |
\((a+x) (b+x) y'(x)=x y(x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 542 |
\(-2 x^3+2 x y(x) y'(x)-y(x)^2+1=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 543 |
\(a+2 x y(x) y'(x)+y(x)^2=0\) Solution method Exact equation Maple ✓ |
| ODE 544 |
\(2 x y(x) y'(x)=a x+y(x)^2\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 545 |
\(x^2+2 x y(x) y'(x)+y(x)^2=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 546 |
\(2 x y(x) y'(x)=x^2+y(x)^2\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 547 |
\(2 x y(x) y'(x)=4 (2 x+1) x^2+y(x)^2\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 548 |
\(x^2 \left (a x^3+1\right )+2 x y(x) y'(x)=6 y(x)^2\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 549 |
\(3 x^2+(2 x y(x)-x+3) y'(x)+y(x)^2-y(x)=0\) Solution method Exact equation Maple ✓ |
| ODE 550 |
\(x (x-2 y(x)) y'(x)+y(x)^2=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 551 |
\(x (2 y(x)+x) y'(x)+(2 x-y(x)) y(x)=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 552 |
\(x (x-2 y(x)) y'(x)+(2 x-y(x)) y(x)=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 553 |
\(x (-2 y(x)+x+1) y'(x)+y(x) (y(x)-2 x+1)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 554 |
\(x (-2 y(x)-x+1) y'(x)+y(x) (y(x)+2 x+1)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 555 |
\(2 x \left (2 x^2+y(x)\right ) y'(x)+y(x) \left (12 x^2+y(x)\right )=0\) Solution method Exact equation Maple ✓ |
| ODE 556 |
\(-3 x^2+2 (x+1) y(x) y'(x)+y(x)^2+2 x=0\) Solution method Exact equation Maple ✓ |
| ODE 557 |
\(x (3 y(x)+2 x) y'(x)=y(x)^2\) Solution method Homogeneous equation Maple ✓ |
| ODE 558 |
\(x (3 y(x)+2 x) y'(x)+3 (y(x)+x)^2=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 559 |
\(\left (x^2+6 x y(x)+3\right ) y'(x)+3 y(x)^2+2 x y(x)+2 x=0\) Solution method Exact equation Maple ✓ |
| ODE 560 |
\(x^3+3 x (2 y(x)+x) y'(x)+3 y(x) (y(x)+2 x)=0\) Solution method Exact equation Maple ✓ |
| ODE 561 |
\(a x y(x) y'(x)=x^2+y(x)^2\) Solution method Homogeneous equation Maple ✓ |
| ODE 562 |
\(a x y(x) y'(x)+x^2-y(x)^2=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 563 |
\(x y'(x) (a+b y(x))=c y(x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 564 |
\(x (x-a y(x)) y'(x)=y(x) (y(x)-a x)\) Solution method Homogeneous equation Maple ✓ |
| ODE 565 |
\(y'(x) (x (A x+B y(x))+\text {a0}+\text {a1} x+\text {a2} y(x))=y(x) (A x+B y(x))+\text {b0}+\text {b1} x+\text {b2} y(x)\) Solution method Homogeneous equation, Jacobi equation Maple ✓ |
| ODE 566 |
\(y'(x) (x (\text {a1}+\text {b2} x+\text {c2} y(x))+\text {a1}+\text {b1} x+\text {c1} y(x))=y(x) (\text {a2}+\text {b2} x+\text {c2} y(x))+\text {a3}+\text {b3} x+\text {c2} y(x)\) Solution method Homogeneous equation, Jacobi equation Maple ✓ |
| ODE 567 |
\(x y'(x) \left (a y(x)+x^n\right )+y(x)^2 (b+c y(x))=0\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 568 |
\(\left (1-x^2 y(x)\right ) y'(x)-x y(x)^2+1=0\) Solution method Exact equation Maple ✓ |
| ODE 569 |
\(\left (1-x^2 y(x)\right ) y'(x)+x y(x)^2-1=0\) Solution method Homogeneous equation, special Maple ✓ |
| ODE 570 |
\(x (1-x y(x)) y'(x)+y(x) (x y(x)+1)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 571 |
\(x (x y(x)+2) y'(x)=2 x^3-x y(x)^2-2 y(x)+3\) Solution method Exact equation Maple ✓ |
| ODE 572 |
\(x (2-x y(x)) y'(x)-x (x y(x)+1) y(x)^2+2 y(x)=0\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 573 |
\(x (3-x y(x)) y'(x)=y(x) (x y(x)-1)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 574 |
\(x^2 (1-y(x)) y'(x)+(1-x) y(x)=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 575 |
\(x^2 (1-y(x)) y'(x)+(x+1) y(x)^2=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 576 |
\(\left (x^2+1\right ) y(x) y'(x)+x \left (1-y(x)^2\right )=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 577 |
\(\left (1-x^2\right ) y(x) y'(x)+2 x^2+x y(x)^2=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 578 |
\(2 x^2 y(x) y'(x)=x^2 (2 x+1)-y(x)^2\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 579 |
\(x (1-2 x y(x)) y'(x)+y(x) (2 x y(x)+1)=0\) Solution method Change of Variable, Two new variables Maple ✓ |
| ODE 580 |
\(x (2 x y(x)+1) y'(x)+y(x) (3 x y(x)+2)=0\) Solution method Homogeneous equation, isobaric equation Maple ✓ |
| ODE 581 |
\(y(x) \left (-x^2 y(x)^2+2 x y(x)+1\right )+x (2 x y(x)+1) y'(x)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 582 |
\(x^2 (x-2 y(x)) y'(x)=2 x^3-4 x y(x)^2+y(x)^3\) Solution method Homogeneous equation Maple ✓ |
| ODE 583 |
\(2 x (x+1) y(x) y'(x)=y(x)^2+1\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 584 |
\(3 x^2 y(x) y'(x)+2 x y(x)^2+1=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 585 |
\(x^2 (4 x-3 y(x)) y'(x)=y(x) \left (6 x^2-3 x y(x)+2 y(x)^2\right )\) Solution method Homogeneous equation Maple ✓ |
| ODE 586 |
\(\left (1-x^3 y(x)\right ) y'(x)=x^2 y(x)^2\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 587 |
\(a+2 x^3 y(x) y'(x)+3 x^2 y(x)^2=0\) Solution method Exact equation Maple ✓ |
| ODE 588 |
\(x \left (3-2 x^2 y(x)\right ) y'(x)=3 x^2 y(x)^2-3 y(x)+4 x\) Solution method Exact equation Maple ✓ |
| ODE 589 |
\(x \left (2 x^2 y(x)+3\right ) y'(x)+y(x) \left (3 x^2 y(x)+4\right )=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 590 |
\(3 x^4+8 x^3 y(x) y'(x)-6 x^2 y(x)^2-y(x)^4=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 591 |
\(x y(x) \left (a+b x^2\right ) y'(x)=A+B y(x)^2\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 592 |
\(3 x^4 y(x) y'(x)=1-2 x^3 y(x)^2\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 593 |
\(x^7 y(x) y'(x)=5 x^3 y(x)+2 \left (x^2+1\right )\) Solution method Abel ODE, Second kind Maple ✓ |
| ODE 594 |
\(\sqrt {x^2+1} y(x) y'(x)+x \sqrt {y(x)^2+1}=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 595 |
\(\sqrt {x^2+1} (y(x)+1) y'(x)=y(x)^3\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 596 |
\(y'(x) (\text {g0}(x)+\text {g1}(x) y(x))=\text {f0}(x)+\text {f1}(x) y(x)+\text {f2}(x) y(x)^2+\text {f3}(x) y(x)^3\) Solution method Abel ODE, Second kind Maple ✗ |
| ODE 597 |
\(y(x)^2 y'(x)+x (2-y(x))=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 598 |
\(y(x)^2 y'(x)=x \left (y(x)^2+1\right )\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 599 |
\(\left (y(x)^2+x\right ) y'(x)+y(x)=a+b x\) Solution method Exact equation Maple ✓ |
| ODE 600 |
\(\left (x-y(x)^2\right ) y'(x)=x^2-y(x)\) Solution method Exact equation Maple ✓ |
| ODE 601 |
\(\left (x^2+y(x)^2\right ) y'(x)+x y(x)=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 602 |
\(\left (x^2+y(x)^2\right ) y'(x)=x y(x)\) Solution method Homogeneous equation Maple ✓ |
| ODE 603 |
\(\left (x^2-y(x)^2\right ) y'(x)=2 x y(x)\) Solution method Homogeneous equation Maple ✓ |
| ODE 604 |
\(\left (x^2-y(x)^2\right ) y'(x)+x (2 y(x)+x)=0\) Solution method Exact equation Maple ✓ |
| ODE 605 |
\(\left (x^2+y(x)^2\right ) y'(x)+2 x (y(x)+2 x)=0\) Solution method Exact equation Maple ✓ |
| ODE 606 |
\(\left (-x^2+y(x)^2+1\right ) y'(x)=x^2-y(x)^2+1\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 607 |
\(\left (a^2+x^2+y(x)^2\right ) y'(x)+2 x y(x)=0\) Solution method Exact equation Maple ✓ |
| ODE 608 |
\(\left (a^2+x^2+y(x)^2\right ) y'(x)+b^2+x^2+2 x y(x)=0\) Solution method Exact equation Maple ✓ |
| ODE 609 |
\(\left (x^2+y(x)^2+x\right ) y'(x)=y(x)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 610 |
\(\left (3 x^2-y(x)^2\right ) y'(x)=2 x y(x)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 611 |
\(\left (x^4+y(x)^2\right ) y'(x)=4 x^3 y(x)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 612 |
\(y(x) (y(x)+1) y'(x)=x (x+1)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 613 |
\(\left (y(x)^2+2 y(x)+x\right ) y'(x)+y(x)^2 (y(x)+x)^2+y(x) (y(x)+1)=0\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 614 |
\(\left (x^2+y(x)^2+2 y(x)\right ) y'(x)+2 x=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 615 |
\(\left (x^3-y(x)^2+2 y(x)\right ) y'(x)+3 x^2 y(x)=0\) Solution method Exact equation Maple ✓ |
| ODE 616 |
\(\left (y(x)^2+x y(x)+y(x)+1\right ) y'(x)+y(x)+1=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 617 |
\((y(x)+x)^2 y'(x)=a^2\) Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\) Maple ✓ |
| ODE 618 |
\((x-y(x))^2 y'(x)=a^2\) Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\) Maple ✓ |
| ODE 619 |
\(\left (x^2+2 x y(x)-y(x)^2\right ) y'(x)+x^2-2 x y(x)+y(x)^2=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 620 |
\((x-y(x))^2 y'(x)=(-y(x)+x+1)^2\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 621 |
\((y(x)+x)^2 y'(x)=(y(x)+x+2)^2\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 622 |
\((y(x)+x)^2 y'(x)=x^2-2 x y(x)+5 y(x)^2\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 623 |
\(y'(x) (a+b+y(x)+x)^2=2 (a+y(x))^2\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 624 |
\(\left (2 x^2+4 x y(x)-y(x)^2\right ) y'(x)=x^2-4 x y(x)-2 y(x)^2\) Solution method Exact equation Maple ✓ |
| ODE 625 |
\((y(x)+3 x)^2 y'(x)=4 y(x) (2 y(x)+3 x)\) Solution method Homogeneous equation Maple ✓ |
| ODE 626 |
\((-y(x)-3 x+1)^2 y'(x)=(-4 y(x)-6 x+3) (1-2 y(x))\) Solution method Change of Variable, Two new variables Maple ✓ |
| ODE 627 |
\(y'(x) \left (\cot (x)-2 y(x)^2\right )=y(x)^3 \csc (x) \sec (x)\) Solution method Change of Variable, new independent variable Maple ✗ |
| ODE 628 |
\(3 y(x)^2 y'(x)=a y(x)^3+x+1\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 629 |
\(\left (x^2-3 y(x)^2\right ) y'(x)+2 x y(x)+1=0\) Solution method Exact equation Maple ✓ |
| ODE 630 |
\(\left (2 x^2+3 y(x)^2\right ) y'(x)+x (y(x)+3 x)=0\) Solution method Exact equation Maple ✓ |
| ODE 631 |
\(3 \left (x^2-y(x)^2\right ) y'(x)-2 y(x)^3+6 x (x+1) y(x)+3 e^x=0\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 632 |
\(\left (3 x^2+2 x y(x)+4 y(x)^2\right ) y'(x)+2 x^2+6 x y(x)+y(x)^2=0\) Solution method Exact equation Maple ✓ |
| ODE 633 |
\((2 y(x)-3 x+1)^2 y'(x)=(-3 y(x)+2 x+4)^2\) Solution method Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \) Maple ✓ |
| ODE 634 |
\(\left (-3 x^2 y(x)+6 y(x)^2+1\right ) y'(x)+x^2-3 x y(x)^2=0\) Solution method Exact equation Maple ✓ |
| ODE 635 |
\(a+(x-6 y(x))^2 y'(x)-6 y(x)^2+2 x y(x)=0\) Solution method Exact equation Maple ✓ |
| ODE 636 |
\(\left (a y(x)^2+x^2\right ) y'(x)=x y(x)\) Solution method Homogeneous equation Maple ✓ |
| ODE 637 |
\(\left (a y(x)^2+x^2+x y(x)\right ) y'(x)=a x^2+x y(x)+y(x)^2\) Solution method Homogeneous equation Maple ✓ |
| ODE 638 |
\(\left (a x^2-a y(x)^2+2 x y(x)\right ) y'(x)-2 a x y(x)+x^2-y(x)^2=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 639 |
\(y'(x) \left (x^2 (a+2 b)+2 x (2 b+c) y(x)+3 c y(x)^2\right )+2 x (a+2 b) y(x)+3 a x^2+(2 b+c) y(x)^2=0\) Solution method Exact equation Maple ✓ |
| ODE 640 |
\(y'(x) \left (a x^2+2 b x y(x)+c y(x)^2\right )+2 a x y(x)+b y(x)^2+k x^2=0\) Solution method Exact equation Maple ✓ |
| ODE 641 |
\(x \left (1-y(x)^2\right ) y'(x)=\left (x^2+1\right ) y(x)\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 642 |
\(x \left (3 x-y(x)^2\right ) y'(x)+y(x) \left (5 x-2 y(x)^2\right )=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 643 |
\(x \left (x^2+y(x)^2\right ) y'(x)=y(x) \left (x^4+x^2+y(x)^2\right )\) Solution method Homogeneous equation, \(xy'(x)=x f(x) g(u)+y(x)\) Maple ✓ |
| ODE 644 |
\(x \left (-x^2+y(x)^2+1\right ) y'(x)+y(x) \left (x^2-y(x)^2+1\right )=0\) Solution method Homogeneous equation, special Maple ✓ |
| ODE 645 |
\(x \left (a-x^2-y(x)^2\right ) y'(x)+y(x) \left (a+x^2+y(x)^2\right )=0\) Solution method Homogeneous equation, special Maple ✓ |
| ODE 646 |
\(x \left (2 x^2+y(x)^2\right ) y'(x)=y(x) \left (2 x^2+3 y(x)^2\right )\) Solution method Homogeneous equation Maple ✓ |
| ODE 647 |
\(\left (x \left (a-x^2-y(x)^2\right )+y(x)\right ) y'(x)-y(x) \left (a-x^2-y(x)^2\right )+x=0\) Solution method Change of Variable, Two new variables Maple ✓ |
| ODE 648 |
\(x (a+y(x))^2 y'(x)=b y(x)^2\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 649 |
\(x \left (x^2-x y(x)+y(x)^2\right ) y'(x)+y(x) \left (x^2+x y(x)+y(x)^2\right )=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 650 |
\(x \left (x^2-x y(x)-y(x)^2\right ) y'(x)=y(x) \left (x^2+x y(x)-y(x)^2\right )\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 651 |
\(x \left (a x y(x)+x^2+y(x)^2\right ) y'(x)=y(x) \left (b x y(x)+x^2+y(x)^2\right )\) Solution method Homogeneous equation Maple ✓ |
| ODE 652 |
\(x \left (x^2-2 y(x)^2\right ) y'(x)=y(x) \left (2 x^2-y(x)^2\right )\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 653 |
\(x \left (x^2+2 y(x)^2\right ) y'(x)=y(x) \left (2 x^2+3 y(x)^2\right )\) Solution method Homogeneous equation Maple ✓ |
| ODE 654 |
\(2 x \left (5 x^2+y(x)^2\right ) y'(x)=x^2 y(x)-y(x)^3\) Solution method Homogeneous equation Maple ✓ |
| ODE 655 |
\(x \left (a x y(x)+x^2+2 y(x)^2\right ) y'(x)=y(x)^2 (a x+2 y(x))\) Solution method Homogeneous equation Maple ✓ |
| ODE 656 |
\(3 x y(x)^2 y'(x)=2 x-y(x)^3\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 657 |
\(\left (3 x y(x)^2-4 x+1\right ) y'(x)=y(x) \left (2-y(x)^2\right )\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 658 |
\(x \left (x-3 y(x)^2\right ) y'(x)+y(x) \left (2 x-y(x)^2\right )=0\) Solution method Exact equation Maple ✓ |
| ODE 659 |
\(x^3+3 x \left (y(x)^2+x\right ) y'(x)-3 x y(x)-2 y(x)^3=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 660 |
\(x \left (-3 x^3 y(x)+x^3+4 y(x)^2\right ) y'(x)=6 y(x)^3\) Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 661 |
\(6 x y(x)^2 y'(x)+2 y(x)^3+x=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 662 |
\(x \left (6 y(x)^2+x\right ) y'(x)-3 y(x)^3+x y(x)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 663 |
\(x \left (x^2-6 y(x)^2\right ) y'(x)=4 y(x) \left (x^2+3 y(x)^2\right )\) Solution method Homogeneous equation Maple ✓ |
| ODE 664 |
\(x \left (3 x-7 y(x)^2\right ) y'(x)+y(x) \left (5 x-3 y(x)^2\right )=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 665 |
\(x^3+x^2 y(x)^2 y'(x)-x+1=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 666 |
\(\left (1-x^2 y(x)^2\right ) y'(x)=x y(x)^3\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 667 |
\(\left (1-x^2 y(x)^2\right ) y'(x)=y(x)^2 (x y(x)+1)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 668 |
\(x \left (x y(x)^2+1\right ) y'(x)+y(x)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 669 |
\(x \left (x y(x)^2+1\right ) y'(x)=y(x) \left (2-3 x y(x)^2\right )\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 670 |
\(x^2 (a+y(x))^2 y'(x)=\left (x^2+1\right ) \left (a^2+y(x)^2\right )\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 671 |
\(\left (x^2+1\right ) \left (y(x)^2+1\right ) y'(x)+2 x y(x) \left (1-y(x)^2\right )=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 672 |
\(\left (x^2+1\right ) \left (y(x)^2+1\right ) y'(x)+2 x y(x) (1-y(x))^2=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 673 |
\(\left (-x^3+6 x^2 y(x)^2+1\right ) y'(x)=x \left (-4 y(x)^3+3 x y(x)+6\right )\) Solution method Exact equation Maple ✓ |
| ODE 674 |
\(x \left (4 x^2 y(x)-12 x y(x)^2+5 x+3\right ) y'(x)+y(x) \left (6 x^2 y(x)-8 x y(x)^2+10 x+3\right )=0\) Solution method Exact equation Maple ✓ |
| ODE 675 |
\(x^3 \left (y(x)^2+1\right ) y'(x)+3 x^2 y(x)=0\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 676 |
\(y(x) \left (x^2 y(x)^2+1\right )+x (1-x y(x))^2 y'(x)=0\) Solution method Homogeneous equation, isobaric equation Maple ✓ |
| ODE 677 |
\(\left (1-x^4 y(x)^2\right ) y'(x)=x^3 y(x)^3\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 678 |
\(\left (3 x-y(x)^3\right ) y'(x)=x^2-3 y(x)\) Solution method Exact equation Maple ✓ |
| ODE 679 |
\(\left (x^3-y(x)^3\right ) y'(x)+x^2 y(x)=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 680 |
\(x^2 (a x+3 y(x))+\left (x^3+y(x)^3\right ) y'(x)=0\) Solution method Exact equation Maple ✓ |
| ODE 681 |
\(\left (-x^2 y(x)-y(x)^3+x\right ) y'(x)=x^3+x y(x)^2-y(x)\) Solution method Exact equation Maple ✓ |
| ODE 682 |
\(\left (a^2 x+y(x) \left (x^2-y(x)^2\right )\right ) y'(x)+x \left (x^2-y(x)^2\right )=a^2 y(x)\) Solution method Change of Variable, Two new variables Maple ✗ |
| ODE 683 |
\(y(x) \left (a+x^2+y(x)^2\right ) y'(x)=x \left (a-x^2-y(x)^2\right )\) Solution method Exact equation Maple ✓ |
| ODE 684 |
\(y(x) \left (3 x^2+y(x)^2\right ) y'(x)+x \left (x^2+3 y(x)^2\right )=0\) Solution method Exact equation Maple ✓ |
| ODE 685 |
\(y(x) \left (a-3 x^2-y(x)^2\right ) y'(x)+x \left (a-x^2+y(x)^2\right )=0\) Solution method Change of Variable, Two new variables Maple ✓ |
| ODE 686 |
\(2 y(x)^3 y'(x)=x^3-x y(x)^2\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 687 |
\(y(x) \left (2 y(x)^2+1\right ) y'(x)=x \left (2 x^2+1\right )\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 688 |
\(x^3+y(x) \left (3 x^2+2 y(x)^2\right ) y'(x)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 689 |
\(y(x) \left (5 x^2+2 y(x)^2\right ) y'(x)+x \left (x^2+5 y(x)^2\right )=0\) Solution method Exact equation Maple ✓ |
| ODE 690 |
\(2 x^3+3 x^2 y(x)+\left (-x^3+x^2+3 x y(x)^2+2 y(x)^3\right ) y'(x)-y(x)^3+y(x)^2=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 691 |
\(4 x^3+9 x^2 y(x)+\left (3 x^3+6 x^2 y(x)-3 x y(x)^2+20 y(x)^3\right ) y'(x)+6 x y(x)^2-y(x)^3=0\) Solution method Exact equation Maple ✓ |
| ODE 692 |
\(\left (a y(x)^3+x^3\right ) y'(x)=x^2 y(x)\) Solution method Homogeneous equation Maple ✓ |
| ODE 693 |
\(y'(x) \left (a x^2-b x^3+3 c x y(x)^2+2 c y(x)^3\right )+a y(x)^2+2 b x^3+3 b x^2 y(x)-c y(x)^3=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 694 |
\(x y(x)^3 y'(x)=\left (1-x^2\right ) \left (y(x)^2+1\right )\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 695 |
\(x \left (x-y(x)^3\right ) y'(x)=y(x) \left (y(x)^3+3 x\right )\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 696 |
\(x \left (2 x^3+y(x)^3\right ) y'(x)=y(x) \left (2 x^3-x^2 y(x)+y(x)^3\right )\) Solution method Homogeneous equation Maple ✓ |
| ODE 697 |
\(x \left (2 x^3-y(x)^3\right ) y'(x)=y(x) \left (x^3-2 y(x)^3\right )\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 698 |
\(x \left (x^3+3 x^2 y(x)+y(x)^3\right ) y'(x)=y(x)^2 \left (3 x^2+y(x)^2\right )\) Solution method Homogeneous equation Maple ✓ |
| ODE 699 |
\(x \left (x^3-2 y(x)^3\right ) y'(x)=y(x) \left (2 x^3-y(x)^3\right )\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 700 |
\(x \left (x^4-2 y(x)^3\right ) y'(x)+y(x) \left (2 x^4+y(x)^3\right )=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 701 |
\(x \left (2 y(x)^3+y(x)+x\right ) y'(x)=(x-y(x)) y(x)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 702 |
\(\left (-7 x y(x)^3-y(x)+5 x\right ) y'(x)-y(x)^4+5 y(x)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 703 |
\(y(x) \left (1-2 x^3 y(x)\right )+x \left (1-2 x y(x)^3\right ) y'(x)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 704 |
\(x \left (-2 x y(x)^3-x y(x)^2+2\right ) y'(x)+2 y(x)+1=0\) Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 705 |
\(\left (-10 x^2 y(x)^3+3 y(x)^2+2\right ) y'(x)=x \left (5 y(x)^4+1\right )\) Solution method Exact equation Maple ✓ |
| ODE 706 |
\(x y'(x) \left (a+b x y(x)^3\right )+y(x) \left (a+c x^3 y(x)\right )=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 707 |
\(y(x) \left (1-2 x^3 y(x)^2\right )+x \left (1-2 x^2 y(x)^3\right ) y'(x)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 708 |
\(x (1-x y(x)) \left (1-x^2 y(x)^2\right ) y'(x)+y(x) (x y(x)+1) \left (x^2 y(x)^2+1\right )=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 709 |
\(\left (x^2-y(x)^4\right ) y'(x)=x y(x)\) Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 710 |
\(\left (x^3-y(x)^4\right ) y'(x)=3 x^2 y(x)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 711 |
\(\left (a^2 x^2+\left (x^2+y(x)^2\right )^2\right ) y'(x)=a^2 x y(x)\) Solution method Change of Variable, Two new variables Maple ✓ |
| ODE 712 |
\(2 \left (x-y(x)^4\right ) y'(x)=y(x)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 713 |
\(\left (-2 y(x)^4-x y(x)^3+4 x\right ) y'(x)=y(x) \left (y(x)^3+2\right )\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 714 |
\(y(x) y'(x) \left ((a x+b y(x))^3+a x^3\right )+x \left ((a x+b y(x))^3+b y(x)^3\right )=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 715 |
\(\left (2 x^2 y(x)^3+x y(x)^4+2 y(x)+x\right ) y'(x)+y(x) \left (y(x)^4+1\right )=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 716 |
\(2 x \left (x^3+y(x)^4\right ) y'(x)=y(x) \left (x^3+2 y(x)^4\right )\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 717 |
\(x \left (1-x^2 y(x)^4\right ) y'(x)+y(x)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 718 |
\(\left (x^2-y(x)^5\right ) y'(x)=2 x y(x)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 719 |
\(x \left (x^3+y(x)^5\right ) y'(x)=y(x) \left (x^3-y(x)^5\right )\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 720 |
\(y(x)^3 \left (3 x^5 y(x)^5-1\right )+x^3 \left (5 x^3 y(x)^7+1\right ) y'(x)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 721 |
\(y'(x) (\text {f1}(x,y(x))+x \text {f2}(x,y(x)))=y(x) \text {f2}(x,y(x))+\text {f3}(x,y(x))\) Solution method Homogeneous equation, Darbooux type Maple ✗ |
| ODE 722 |
\(y'(x) (a (y(x)+x)+1)^n+a (y(x)+x)^n=0\) Solution method Exact equation Maple ✓ |
| ODE 723 |
\(x y'(x) \left (a+x y(x)^n\right )+b y(x)=0\) Solution method Change of Variable, new independent variable Maple ✓ |
| ODE 724 |
\(f(x) y(x)^m y'(x)+g(x) y(x)^{m+1}+h(x) y(x)^n=0\) Solution method The Bernoulli ODE Maple ✓ |
| ODE 725 |
\(\sqrt {b^2+y(x)^2} y'(x)=\sqrt {a^2+x^2}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 726 |
\(\sqrt {b^2-y(x)^2} y'(x)=\sqrt {a^2-x^2}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 727 |
\(\sqrt {Y} y'(x)=\sqrt {X}\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 728 |
\(\left (\sqrt {y(x)+x}+1\right ) y'(x)+1=0\) Solution method Change of Variable, new dependent variable Maple ✓ |
| ODE 729 |
\(\sqrt {x y(x)} y'(x)-y(x)+x=\sqrt {x y(x)}\) Solution method Homogeneous equation Maple ✓ |
| ODE 730 |
\(\left (x-2 \sqrt {x y(x)}\right ) y'(x)=y(x)\) Solution method Homogeneous equation Maple ✓ |
| ODE 731 |
\(\left (x^2+1\right )^{3/2} \left (y(x)+\sqrt {y(x)^2+1}\right ) y'(x)=y(x)^2+1\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 732 |
\(\left (x^2+1\right )^{3/2} \left (y(x)+\sqrt {y(x)^2+1}\right ) y'(x)=y(x)^2+1\) Solution method Separable ODE, Neither variable missing Maple ✓ |
| ODE 733 |
\(\left (x-\sqrt {x^2+y(x)^2}\right ) y'(x)=y(x)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 734 |
\(x \left (1-\sqrt {x^2-y(x)^2}\right ) y'(x)=y(x)\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 735 |
\(x \left (\sqrt {x^2+y(x)^2}+x\right ) y'(x)+\sqrt {x^2+y(x)^2} y(x)=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 736 |
\(x y(x) \left (\sqrt {x^2-y(x)^2}+x\right ) y'(x)=x y(x)^2-\left (x^2-y(x)^2\right )^{3/2}\) Solution method Homogeneous equation Maple ✓ |
| ODE 737 |
\(\left (x-y(x)^2 \sqrt {y(x)^2-x^2}\right ) y'(x)=y(x) \left (x \sqrt {y(x)^2-x^2}+1\right )\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 738 |
\(\left (x \sqrt {x^2+y(x)^2+1}-y(x) \left (x^2+y(x)^2\right )\right ) y'(x)=\sqrt {x^2+y(x)^2+1} y(x)+x \left (x^2+y(x)^2\right )\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 739 |
\(y'(x) \left (x^2 \sec (x) \cos (y(x))+1\right )-y(x) \tan (x)+\sec (x) \sin (y(x))=0\) Solution method Exact equation, integrating factor Maple ✗ |
| ODE 740 |
\(y'(x) \cos (y(x)) (\cos (y(x))-\sin (A) \sin (x))+\cos (x) (\cos (x)-\sin (A) \sin (y(x)))=0\) Solution method Exact equation Maple ✓ |
| ODE 741 |
\(y'(x) (a \cos (a y(x)+b x)-b \sin (a x+b y(x)))-a \sin (a x+b y(x))+b \cos (a y(x)+b x)=0\) Solution method Exact equation Maple ✓ |
| ODE 742 |
\(y'(x) (a \sin (x y(x))-\sin (y(x))+\cos (y(x)+x))+y(x) \sin (x y(x))+\cos (y(x)+x)+\cos (x)=0\) Solution method Exact equation Maple ✗ |
| ODE 743 |
\(y'(x) (\cos (x) \sec (y(x))+x)+\tan (y(x))-y(x) \sin (x) \sec (y(x))=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 744 |
\(y'(x) \left (x^2+2 y(x) \sin (x) \sec (y(x))\right )+2 x \tan (y(x))+y(x)^2 \cos (x) \sec (y(x))=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 745 |
\(y'(x) \left (x^2 \sec ^2(y(x))-6 x y(x)+2\right )-3 y(x)^2+2 x \tan (y(x))=0\) Solution method Exact equation Maple ✓ |
| ODE 746 |
\(y'(x) ((y(x)+x) \tan (y(x))+1)+1=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 747 |
\(x y'(x) \left (x-y(x) \tan \left (\frac {y(x)}{x}\right )\right )+y(x) \left (y(x) \tan \left (\frac {y(x)}{x}\right )+x\right )=0\) Solution method Homogeneous equation Maple ✓ |
| ODE 748 |
\(\left (x e^{y(x)}+e^x\right ) y'(x)+e^x y(x)+e^{y(x)}=0\) Solution method Exact equation Maple ✓ |
| ODE 749 |
\(y'(x) (-\log (y(x))-2 x+1)+2 y(x)=0\) Solution method Exact equation, integrating factor Maple ✓ |
| ODE 750 |
\(y'(x) (x \cosh (y(x))+\sinh (x))+\sinh (y(x))+y(x) \cosh (x)=0\) Solution method Exact equation Maple ✓ |
| ODE 751 |
\((\sinh (x)+1) y'(x) \sinh (y(x))+\cosh (x) (\cosh (y(x))-1)=0\) Solution method Exact equation Maple ✓ |
| ODE 752 |
\(y'(x)^2=a x^n\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 753 |
\(y'(x)^2=y(x)\) Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 754 |
\(y'(x)^2=x-y(x)\) Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 755 |
\(y'(x)^2=x^2+y(x)\) Solution method Homogeneous ODE, The Isobaric equation Maple ✓ |
| ODE 756 |
\(x^2+y'(x)^2=4 y(x)\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 757 |
\(3 x^2+y'(x)^2=8 y(x)\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 758 |
\(a x^2+b y(x)+y'(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 759 |
\(y'(x)^2=y(x)^2+1\) Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 760 |
\(y'(x)^2=1-y(x)^2\) Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 761 |
\(y'(x)^2=a^2-y(x)^2\) Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 762 |
\(y'(x)^2=a^2 y(x)^2\) Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 763 |
\(y'(x)^2=a+b y(x)^2\) Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 764 |
\(y'(x)^2=x^2 y(x)^2\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 765 |
\(y'(x)^2=(y(x)-1) y(x)^2\) Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 766 |
\(y'(x)^2=(y(x)-a) (y(x)-b) (y(x)-c)\) Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 767 |
\(y'(x)^2=a^2 y(x)^n\) Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 768 |
\(y'(x)^2=a^2 y(x)^2 \left (1-\log ^2(y(x))\right )\) Solution method Change of variable Maple ✓ |
| ODE 769 |
\(f(x) (y(x)-a) (y(x)-b)+y'(x)^2=0\) Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 770 |
\(f(x) (y(x)-a)^2 (y(x)-b)+y'(x)^2=0\) Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 771 |
\(f(x) (y(x)-a) (y(x)-b) (y(x)-c)+y'(x)^2=0\) Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 772 |
\(f(x) (y(x)-a)^2 (y(x)-b) (y(x)-c)+y'(x)^2=0\) Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 773 |
\(f(x) (y(x)-\text {a1}) (y(x)-\text {a2}) (y(x)-\text {a3}) (y(x)-\text {a4})+y'(x)^2=0\) Solution method Binomial equation \((y')^m + F(x) G(y)=0\) Maple ✓ |
| ODE 774 |
\(y'(x)^2=f(x)^2 (y(x)-a) (y(x)-b) (y(x)-c)^2\) Solution method Change of variable Maple ✓ |
| ODE 775 |
\(y'(x)^2=f(x)^2 (y(x)-a) (y(x)-b) (y(x)-u(x))^2\) Solution method Change of variable Maple ✗ |
| ODE 776 |
\(y'(x)^2+2 y'(x)+x=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 777 |
\(a (x-y(x))+y'(x)^2-2 y'(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 778 |
\(y'(x)^2-2 y'(x)-y(x)^2=0\) Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 779 |
\(y'(x)^2-5 y'(x)+6=0\) Solution method Missing Variables ODE, Both independent and dependent
variable missing Maple ✓ |
| ODE 780 |
\(y'(x)^2-7 y'(x)+12=0\) Solution method Missing Variables ODE, Both independent and dependent
variable missing Maple ✓ |
| ODE 781 |
\(a y'(x)+b+y'(x)^2=0\) Solution method Missing Variables ODE, Both independent and dependent
variable missing Maple ✓ |
| ODE 782 |
\(a y'(x)+b x+y'(x)^2=0\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(x\) Maple ✓ |
| ODE 783 |
\(a y'(x)+b y(x)+y'(x)^2=0\) Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y\) Maple ✓ |
| ODE 784 |
\(y'(x)^2+x y'(x)+1=0\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(x\) Maple ✓ |
| ODE 785 |
\(y'(x)^2+x y'(x)-y(x)=0\) Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 786 |
\(y'(x)^2-x y'(x)+y(x)=0\) Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 787 |
\(y'(x)^2-x y'(x)-y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 788 |
\(y'(x)^2+x y'(x)-y(x)+x=0\) Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 789 |
\(y'(x)^2+(1-x) y'(x)+y(x)=0\) Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 790 |
\(y'(x)^2-(x+1) y'(x)+y(x)=0\) Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 791 |
\(y'(x)^2-(2-x) y'(x)-y(x)+1=0\) Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 792 |
\((a+x) y'(x)+y'(x)^2-y(x)=0\) Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 793 |
\(y'(x)^2-2 x y'(x)+1=0\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(x\) Maple ✓ |
| ODE 794 |
\(-3 x^2+2 x y'(x)+y'(x)^2=0\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 795 |
\(y'(x)^2+2 x y'(x)-y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 796 |
\(y'(x)^2+2 x y'(x)-y(x)=0\) Solution method Change of variable Maple ✓ |
| ODE 797 |
\(y'(x)^2-2 x y'(x)+2 y(x)=0\) Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 798 |
\(y'(x)^2-(2 x+1) y'(x)-(1-x) x=0\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 799 |
\(y'(x)^2+2 (1-x) y'(x)-2 (x-y(x))=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 800 |
\(y'(x)^2+3 x y'(x)-y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 801 |
\(y'(x)^2-4 (x+1) y'(x)+4 y(x)=0\) Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 802 |
\(a x y'(x)+y'(x)^2=b c x^2\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 803 |
\(-a x y'(x)+a y(x)+y'(x)^2=0\) Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 804 |
\(a x y'(x)+b x^2+c y(x)+y'(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 805 |
\((a+b x) y'(x)+c+y'(x)^2=b y(x)\) Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 806 |
\(-2 x^2 y'(x)+2 x y'(x)+y'(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 807 |
\(a x^2 y'(x)+b x y(x)+y'(x)^2=0\) Solution method Homogeneous ODE, The Isobaric equation Maple ✓ |
| ODE 808 |
\(a x^3 y'(x)-2 a x^2 y(x)+y'(x)^2=0\) Solution method Homogeneous ODE, The Isobaric equation Maple ✓ |
| ODE 809 |
\(-2 a x^3 y'(x)+4 a x^2 y(x)+y'(x)^2=0\) Solution method Change of variable Maple ✓ |
| ODE 810 |
\(4 x^5 y'(x)-12 x^4 y(x)+y'(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 811 |
\(y'(x)^2-2 \cosh (x) y'(x)+1=0\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 812 |
\(y'(x)^2+y(x) y'(x)=x (y(x)+x)\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 813 |
\(y'(x)^2-y(x) y'(x)+e^x=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 814 |
\(y'(x)^2+(y(x)+x) y'(x)+x y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 815 |
\(y'(x)^2-2 y(x) y'(x)-2 x=0\) Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 816 |
\(y'(x)^2+(2 y(x)+1) y'(x)+(y(x)-1) y(x)=0\) Solution method Missing Variables ODE, Independent variable missing, Use new
variable Maple ✓ |
| ODE 817 |
\(y'(x)^2-2 (x-y(x)) y'(x)-4 x y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 818 |
\(y'(x)^2-(4 y(x)+1) y'(x)+y(x) (4 y(x)+1)=0\) Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 819 |
\(y'(x)^2-2 (1-3 y(x)) y'(x)-(4-9 y(x)) y(x)=0\) Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 820 |
\(y(x) (3 a+b+9 y(x))+(a+6 y(x)) y'(x)+y'(x)^2=0\) Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 821 |
\(a y(x) y'(x)-a x+y'(x)^2=0\) Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 822 |
\(-a y(x) y'(x)-a x+y'(x)^2=0\) Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 823 |
\(y'(x) (a x+b y(x))+a b x y(x)+y'(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 824 |
\(y(x)^2 \log (a y(x))-x y(x) y'(x)+y'(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 825 |
\(y'(x)^2-(2 x y(x)+1) y'(x)+2 x y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 826 |
\(y'(x)^2-\left (y(x)^2+4\right ) y'(x)+y(x)^2+4=0\) Solution method Missing Variables ODE, Independent variable missing, Use new
variable Maple ✓ |
| ODE 827 |
\(-(x-y(x)) y(x) y'(x)+y'(x)^2-x y(x)^3=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 828 |
\(x y(x)^2 y'(x)+y'(x)^2+y(x)^3=0\) Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 829 |
\(-2 x^3 y(x)^2 y'(x)-4 x^2 y(x)^3+y'(x)^2=0\) Solution method Change of variable Maple ✓ |
| ODE 830 |
\(x^4 y(x)^4-x \left (x^2+y(x)^2\right ) y(x) y'(x)+y'(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 831 |
\(2 x y(x)^3 y'(x)+y'(x)^2+y(x)^4=0\) Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 832 |
\(y'(x)^2+2 y(x) \cot (x) y'(x)-y(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 833 |
\(y'(x)^2-3 x y(x)^{2/3} y'(x)+9 y(x)^{5/3}=0\) Solution method Change of variable Maple ✓ |
| ODE 834 |
\(y'(x)^2=e^{4 x-2 y(x)} \left (y'(x)-1\right )\) Solution method Change of variable Maple ✓ |
| ODE 835 |
\(2 y'(x)^2+x y'(x)-2 y(x)=0\) Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 836 |
\(2 y'(x)^2-(1-x) y'(x)-y(x)=0\) Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 837 |
\(-2 x^2 y'(x)+2 y'(x)^2+3 x y(x)=0\) Solution method Homogeneous ODE, The Isobaric equation Maple ✓ |
| ODE 838 |
\(2 y'(x)^2+2 (6 y(x)-1) y'(x)+3 y(x) (6 y(x)-1)=0\) Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 839 |
\(3 y'(x)^2-2 x y'(x)+y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 840 |
\(x^2+4 x y'(x)+3 y'(x)^2-y(x)=0\) Solution method Change of variable Maple ✓ |
| ODE 841 |
\(4 y'(x)^2=9 x\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 842 |
\(4 y'(x)^2+2 x e^{-2 y(x)} y'(x)-e^{-2 y(x)}=0\) Solution method Change of variable Maple ✓ |
| ODE 843 |
\(4 y'(x)^2+2 e^{2 x-2 y(x)} y'(x)-e^{2 x-2 y(x)}=0\) Solution method Change of variable Maple ✓ |
| ODE 844 |
\(5 y'(x)^2+3 x y'(x)-y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 845 |
\(5 y'(x)^2+6 x y'(x)-2 y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 846 |
\(3 x y(x)^4 y'(x)+9 y'(x)^2+y(x)^5=0\) Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 847 |
\(x y'(x)^2=a\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 848 |
\(x y'(x)^2=a-x^2\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 849 |
\(x y'(x)^2=y(x)\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 850 |
\(x y'(x)^2-2 y(x)+x=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 851 |
\(x y'(x)^2+y'(x)=y(x)\) Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 852 |
\(x y'(x)^2+2 y'(x)-y(x)=0\) Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 853 |
\(x y'(x)^2-2 y'(x)-y(x)=0\) Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 854 |
\(x y'(x)^2+4 y'(x)-2 y(x)=0\) Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 855 |
\(x y'(x)^2+x y'(x)-y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 856 |
\(-\left (x^2+1\right ) y'(x)+x y'(x)^2+x=0\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 857 |
\(a+x y'(x)^2+y(x) y'(x)=0\) Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 858 |
\(a+x y'(x)^2-y(x) y'(x)=0\) Solution method Clairaut’s equation and related types, main form Maple ✓ |
| ODE 859 |
\(a x+x y'(x)^2-y(x) y'(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 860 |
\(-x^2+x y'(x)^2+y(x) y'(x)=0\) Solution method Homogeneous ODE, The Isobaric equation Maple ✓ |
| ODE 861 |
\(x^3+x y'(x)^2+y(x) y'(x)=0\) Solution method Homogeneous ODE, The Isobaric equation Maple ✓ |
| ODE 862 |
\(a y(x)+x y'(x)^2-y(x) y'(x)=0\) Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 863 |
\(y(x) y'(x)+x y'(x)^2-y(x)^4=0\) Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 864 |
\((a-y(x)) y'(x)+b+x y'(x)^2=0\) Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 865 |
\(x y'(x)^2+(x-y(x)) y'(x)-y(x)+1=0\) Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 866 |
\((a-y(x)+x) y'(x)+x y'(x)^2-y(x)=0\) Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 867 |
\(x y'(x)^2-(3 x-y(x)) y'(x)+y(x)=0\) Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 868 |
\(a-b y(x)+b x+x y'(x)^2-y(x)=0\) Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 869 |
\(a+x y'(x)^2-2 y(x) y'(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 870 |
\(x y'(x)^2+2 y(x) y'(x)-x=0\) Solution method Homogeneous ODE, \(x^n f\left (\frac {y}{x} , y' \right )=0\), Solve for \(p\) Maple ✓ |
| ODE 871 |
\(a x+x y'(x)^2-2 y(x) y'(x)=0\) Solution method Homogeneous ODE, \(x^n f\left (\frac {y}{x} , y' \right )=0\), Solve for \(y\) Maple ✓ |
| ODE 872 |
\(x y'(x)^2-2 y(x) y'(x)+2 y(x)+x=0\) Solution method Change of variable Maple ✓ |
| ODE 873 |
\(9 x^2+x y'(x)^2-3 y(x) y'(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 874 |
\(x y'(x)^2-(3 y(x)+2 x) y'(x)+6 y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 875 |
\(-a y(x) y'(x)+b+x y'(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 876 |
\(a y(x) y'(x)+b x+x y'(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 877 |
\(x y'(x)^2-(x y(x)+1) y'(x)+y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 878 |
\((1-x) y(x) y'(x)+x y'(x)^2-y(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 879 |
\(\left (1-x^2 y(x)\right ) y'(x)+x y'(x)^2-x y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 880 |
\((x+1) y'(x)^2=y(x)\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 881 |
\((x+1) y'(x)^2-(y(x)+x) y'(x)+y(x)=0\) Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 882 |
\((a-x) y'(x)^2-b+y(x) y'(x)=0\) Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 883 |
\((a+x) y'(x)^2+y'(x) (\text {a1}+\text {b1} x+\text {c1} y(x))+\text {a2}+\text {b2} x+\text {c2} y(x)=0\) Solution method Change of variable Maple ✓ |
| ODE 884 |
\(2 x y'(x)^2+(2 x-y(x)) y'(x)-y(x)+1=0\) Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 885 |
\(3 x y'(x)^2-6 y(x) y'(x)+2 y(x)+x=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 886 |
\((3 x+1) y'(x)^2-3 (y(x)+2) y'(x)+9=0\) Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 887 |
\((3 x+5) y'(x)^2-(3 y(x)+3) y'(x)+y(x)=0\) Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 888 |
\(4 x y'(x)^2=(a-3 x)^2\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 889 |
\(4 x y'(x)^2+2 x y'(x)-y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 890 |
\(4 x y'(x)^2-3 y(x) y'(x)+3=0\) Solution method Clairaut’s equation and related types, d’Alembert’s equation
(also call Lagrange’s) Maple ✓ |
| ODE 891 |
\(4 x y'(x)^2+4 y(x) y'(x)=1\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 892 |
\(4 y(x) y'(x)+4 x y'(x)^2-y(x)^4=0\) Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 893 |
\(4 (2-x) y'(x)^2+1=0\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 894 |
\(8 y(x) y'(x)+16 x y'(x)^2+y(x)^6=0\) Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 895 |
\(x^2 y'(x)^2=a^2\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 896 |
\(x^2 y'(x)^2=y(x)^2\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 897 |
\(x^2 y'(x)^2+x^2-y(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 898 |
\(x^2 y'(x)^2=(x-y(x))^2\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 899 |
\(x^2 y'(x)^2-y(x)^4+y(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 900 |
\(x^2 y'(x)^2-x y'(x)+(1-y(x)) y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 901 |
\(a^2+2 a x y'(x)-2 a y(x)+x^2 y'(x)^2+x^2=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 902 |
\(x^2 y'(x)^2-2 x y(x) y'(x)+y(x) (y(x)+1)-x=0\) Solution method Change of variable Maple ✓ |
| ODE 903 |
\(-x^4+x^2 y'(x)^2+\left (1-x^2\right ) y(x)^2-2 x y(x) y'(x)=0\) Solution method Change of variable Maple ✓ |
| ODE 904 |
\(x^2 y'(x)^2-(2 x y(x)+1) y'(x)+y(x)^2+1=0\) Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 905 |
\(-(a+2 x y(x)) y'(x)+x^2 y'(x)^2+y(x)^2=0\) Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 906 |
\(x^2 y'(x)^2-x (x-2 y(x)) y'(x)+y(x)^2=0\) Solution method Change of variable Maple ✓ |
| ODE 907 |
\(-4 a+x^2 y'(x)^2+2 x (y(x)+2 x) y'(x)+y(x)^2=0\) Solution method Change of variable Maple ✓ |
| ODE 908 |
\(x \left (x^3-2 y(x)\right ) y'(x)-\left (2 x^3-y(x)\right ) y(x)+x^2 y'(x)^2=0\) Solution method Change of variable Maple ✓ |
| ODE 909 |
\(x^2 y'(x)^2+3 x y(x) y'(x)+2 y(x)^2=0\) Solution method Homogeneous ODE, \(x^n f\left (\frac {y}{x} , y' \right )=0\), Solve for \(p\) Maple ✓ |
| ODE 910 |
\(x^3+x^2 y'(x)^2-3 x y(x) y'(x)+2 y(x)^2=0\) Solution method Change of variable Maple ✓ |
| ODE 911 |
\(x^2 y'(x)^2+4 x y(x) y'(x)-5 y(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 912 |
\(x^2 y'(x)^2-4 x (y(x)+2) y'(x)+4 y(x) (y(x)+2)=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 913 |
\(x^2 y'(x)^2-5 x y(x) y'(x)+6 y(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 914 |
\(x^2 y'(x)^2+x \left (x^2+x y(x)-2 y(x)\right ) y'(x)+(1-x) \left (x^2-y(x)\right ) y(x)=0\) Solution method Change of variable Maple ✗ |
| ODE 915 |
\(x^2 y'(x)^2+(y(x)+2 x) y(x) y'(x)+y(x)^2=0\) Solution method Change of variable Maple ✓ |
| ODE 916 |
\(x^2 y'(x)^2+(2 x-y(x)) y(x) y'(x)+y(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 917 |
\(y'(x) \left (a+b x^2 y(x)^3\right )+a b y(x)^3+x^2 y'(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 918 |
\(\left (1-x^2\right ) y'(x)^2=1-y(x)^2\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 919 |
\(\left (1-x^2\right ) y'(x)^2+4 x^2+2 x y(x) y'(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 920 |
\(\left (a^2+x^2\right ) y'(x)^2=b^2\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 921 |
\(\left (a^2-x^2\right ) y'(x)^2+b^2=0\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 922 |
\(\left (a^2-x^2\right ) y'(x)^2=b^2\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 923 |
\(\left (a^2-x^2\right ) y'(x)^2=x^2\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 924 |
\(\left (a^2-x^2\right ) y'(x)^2+x^2+2 x y(x) y'(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 925 |
\(\left (a^2-x^2\right ) y'(x)^2-2 x y(x) y'(x)-y(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 926 |
\(\left (a^2+x^2\right ) y'(x)^2+b-2 x y(x) y'(x)+y(x)^2=0\) Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\) Maple ✓ |
| ODE 927 |
\(\left (2 x^2+1\right ) y'(x)^2+\left (x^2+2 x y(x)+y(x)^2+2\right ) y'(x)+2 y(x)^2+1=0\) Solution method Change of variable Maple ✓ |
| ODE 928 |
\(4 x^2 y'(x)^2-4 x y(x) y'(x)=8 x^3-y(x)^2\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 929 |
\(a x^2 y'(x)^2+(1-a) a x^2-2 a x y(x) y'(x)+y(x)^2=0\) Solution method Homogeneous ODE, \(x^n f\left (\frac {y}{x} , y' \right )=0\), Solve for \(p\) Maple ✓ |
| ODE 930 |
\(\left (1-a^2\right ) x^2 y'(x)^2-a^2 x^2-2 x y(x) y'(x)+y(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 931 |
\(x^3 y'(x)^2=a\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 932 |
\(x^3 y'(x)^2+x y'(x)-y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 933 |
\(a+x^3 y'(x)^2+x^2 y(x) y'(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 934 |
\(x^3 y'(x)^2-\left (2 x^2 y(x)+1\right ) y'(x)+x y(x)^2=0\) Solution method Change of variable Maple ✓ |
| ODE 935 |
\(x \left (1-x^2\right ) y'(x)^2-2 \left (1-x^2\right ) y(x) y'(x)+x \left (1-y(x)^2\right )=0\) Solution method Change of variable Maple ✓ |
| ODE 936 |
\(4 x (a-x) (b-x) y'(x)^2=\left (-2 x (a+b)+a b+2 x^2\right )^2\) Solution method Change of variable Maple ✓ |
| ODE 937 |
\(x^4 y'(x)^2-x y'(x)-y(x)=0\) Solution method Homogeneous ODE, The Isobaric equation Maple ✓ |
| ODE 938 |
\(x^4 y'(x)^2+2 x^3 y(x) y'(x)-4=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 939 |
\(x^4 y'(x)^2+x y(x)^2 y'(x)-y(x)^3=0\) Solution method Change of variable Maple ✓ |
| ODE 940 |
\(x^2 \left (a^2-x^2\right ) y'(x)^2+1=0\) Solution method Missing Variables ODE, Dependent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 941 |
\(3 x^4 y'(x)^2-x y(x)-y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 942 |
\(4 x^5 y'(x)^2+12 x^4 y(x) y'(x)+9=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 943 |
\(x^6 y'(x)^2-2 x y'(x)-4 y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 944 |
\(x^8 y'(x)^2+3 x y'(x)+9 y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 945 |
\(y(x) y'(x)^2=a\) Solution method Missing Variables ODE, Independent variable missing, Solve for
\(y'\) Maple ✓ |
| ODE 946 |
\(y(x) y'(x)^2=a^2 x\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 947 |
\(y(x) y'(x)^2=e^{2 x}\) Solution method Change of variable Maple ✓ |
| ODE 948 |
\(2 a x y'(x)-a y(x)+y(x) y'(x)^2=0\) Solution method Homogeneous ODE, \(x^n f\left (\frac {y}{x} , y' \right )=0\) Maple ✓ |
| ODE 949 |
\(-4 a^2 x y'(x)+a^2 y(x)+y(x) y'(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 950 |
\(a x y'(x)+b y(x)+y(x) y'(x)^2=0\) Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 951 |
\(-(a-2 b x) y'(x)-b y(x)+y(x) y'(x)^2=0\) Solution method Change of variable Maple ✓ |
| ODE 952 |
\(x^3 y'(x)-x^2 y(x)+y(x) y'(x)^2=0\) Solution method Change of variable Maple ✓ |
| ODE 953 |
\(y(x) y'(x)^2+(x-y(x)) y'(x)-x=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 954 |
\(y(x) y'(x)^2-(y(x)+x) y'(x)+y(x)=0\) Solution method No Missing Variables ODE, Solve for \(x\) Maple ✓ |
| ODE 955 |
\(y(x) y'(x)^2-(x y(x)+1) y'(x)+x=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 956 |
\(y(x) y'(x)^2+\left (x-y(x)^2\right ) y'(x)-x y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y'\) Maple ✓ |
| ODE 957 |
\(y(x) y'(x)^2+y(x)=a\) Solution method Missing Variables ODE, Independent variable missing, Use new
variable Maple ✓ |
| ODE 958 |
\((y(x)+x) y'(x)^2+2 x y'(x)-y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 959 |
\((2 x-y(x)) y'(x)^2-2 (1-x) y'(x)-y(x)+2=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 960 |
\(2 y(x) y'(x)^2+(5-4 x) y'(x)+2 y(x)=0\) Solution method No Missing Variables ODE, Solve for \(y\) Maple ✓ |
| ODE 961 |
\(4 x^3 y'(x)-4 x^2 y(x)+9 y(x) y'(x)^2=0\) Solution method Change of variable Maple ✓ |
| ODE 962 |
\((1-a y(x)) y'(x)^2=a y(x)\) Solution method Missing Variables ODE, Independent variable missing, Use new
variable Maple ✓ |
| ODE 963 |
\(y'(x)^2 (\text {a0}+\text {b0} x+\text {c0} y(x))+y'(x) (\text {a1}+\text {b1} x+\text {c1} y(x))+\text {a2}+\text {b2} x+\text {c2} y(x)=0\) Solution method Change of variable Maple ✓ |