| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\frac {-y+y^{\prime } x}{\sqrt {x^{2}-y^{2}}}&=y^{\prime } x \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
6.492 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.223 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.207 |
|
| \begin{align*}
x -y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.921 |
|
| \begin{align*}
-y+y^{\prime } x&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.395 |
|
| \begin{align*}
3 x^{2}+6 y x +3 y^{2}+\left (2 x^{2}+3 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.341 |
|
| \begin{align*}
\left (x^{2}+2 y+y^{2}\right ) y^{\prime }+2 x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
2.224 |
|
| \begin{align*}
y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.918 |
|
| \begin{align*}
x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| \begin{align*}
y^{2}-x^{2}+2 m x y+\left (m y^{2}-m \,x^{2}-2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.129 |
|
| \begin{align*}
y^{\prime } x -y+2 x^{2} y-x^{3}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.987 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }-1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.496 |
|
| \begin{align*}
x +y y^{\prime }+y-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.950 |
|
| \begin{align*}
y^{\prime } x -a y+b y^{2}&=c \,x^{2 a} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.264 |
|
| \begin{align*}
x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.982 |
|
| \begin{align*}
y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.390 |
|
| \begin{align*}
y^{\prime }-x^{2} y&=x^{5} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.457 |
|
| \begin{align*}
\left (-x +y\right )^{2} y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.905 |
|
| \begin{align*}
y^{\prime } x +y+{\mathrm e}^{x} x^{4} y^{4}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.960 |
|
| \begin{align*}
x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.394 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.809 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.326 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.865 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.191 |
|
| \begin{align*}
\left (4+2 x -y\right ) y^{\prime }+5+x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.545 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
7.769 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.152 |
|
| \begin{align*}
x y^{2} \left (y^{\prime } x +3 y\right )-2 y+y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
14.563 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y&=\arctan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.299 |
|
| \begin{align*}
5 y x -3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
5.724 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.312 |
|
| \begin{align*}
y+x y^{2}-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.889 |
|
| \begin{align*}
\left (1-x \right ) y-x \left (1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.576 |
|
| \begin{align*}
3 x^{2} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.725 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) \left (x +y y^{\prime }\right )&=\left (x^{2}+y^{2}+x \right ) \left (-y+y^{\prime } x \right ) \\
\end{align*} |
[_rational] |
✗ |
✓ |
✓ |
✗ |
5.239 |
|
| \begin{align*}
2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.557 |
|
| \begin{align*}
y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.178 |
|
| \begin{align*}
2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.914 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) \left (x +y y^{\prime }\right )+\sqrt {1+x^{2}+y^{2}}\, \left (-y^{\prime } x +y\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
8.063 |
|
| \begin{align*}
1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.615 |
|
| \begin{align*}
y^{\prime } x -y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.362 |
|
| \begin{align*}
x^{3} y^{4}+x^{2} y^{3}+x y^{2}+y+\left (y^{3} x^{4}-x^{3} y^{2}-x^{3} y+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
3.338 |
|
| \begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.743 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.498 |
|
| \begin{align*}
x {y^{\prime }}^{2}-2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| \begin{align*}
\left (2 y^{\prime } x -y\right )^{2}&=8 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| \begin{align*}
\left (x^{2}+1\right ) {y^{\prime }}^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (y^{2}+2 x \right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| \begin{align*}
2 y^{\prime } x -y+\ln \left (y^{\prime }\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.729 |
|
| \begin{align*}
4 x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.621 |
|
| \begin{align*}
x {y^{\prime }}^{2}-2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.145 |
|
| \begin{align*}
y^{\prime }+2 y x&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| \begin{align*}
y&=-y^{\prime } x +x^{4} {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
1.427 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.164 |
|
| \begin{align*}
x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
4.868 |
|
| \begin{align*}
a^{2} y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| \begin{align*}
x {y^{\prime }}^{2}-2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.171 |
|
| \begin{align*}
{y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
0.793 |
|
| \begin{align*}
\left (-y+y^{\prime } x \right )^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.758 |
|
| \begin{align*}
4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 y^{\prime } x -1&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.740 |
|
| \begin{align*}
4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.746 |
|
| \begin{align*}
{\mathrm e}^{2 y} {y^{\prime }}^{3}+\left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
30.007 |
|
| \begin{align*}
x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
2.578 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
120.403 |
|
| \begin{align*}
y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.797 |
|
| \begin{align*}
a^{2} y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.880 |
|
| \begin{align*}
\left (x -y^{\prime }-y\right )^{2}&=x^{2} \left (2 y x -x^{2} y^{\prime }\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
66.469 |
|
| \begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )&=a^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| \begin{align*}
y y^{\prime }&=\left (x -b \right ) {y^{\prime }}^{2}+a \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.529 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
1.556 |
|
| \begin{align*}
3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.701 |
|
| \begin{align*}
y&=\left (x +1\right ) {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.457 |
|
| \begin{align*}
\left (-y+y^{\prime } x \right ) \left (x +y y^{\prime }\right )&=a^{2} y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✗ |
✓ |
✗ |
77.483 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.698 |
|
| \begin{align*}
\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 y y^{\prime } x +y^{2}-1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.714 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-2 \left (y x +2 y^{\prime }\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {y {y^{\prime }}^{2}}{x^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.556 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x +y^{2}&=y^{2} x^{2}+x^{4} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
8.677 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {1}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.394 |
|
| \begin{align*}
x {y^{\prime }}^{2}-2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.144 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-2 \left (y x -2\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
1.362 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-\left (x -1\right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
8 \left (1+y^{\prime }\right )^{3}&=27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
26.139 |
|
| \begin{align*}
4 {y^{\prime }}^{2}&=9 x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.716 |
|
| \begin{align*}
y \left (3-4 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.261 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.085 |
|
| \begin{align*}
2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
4 y^{\prime \prime \prime }-3 y^{\prime }+y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| \begin{align*}
-y-2 y^{\prime }+2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.060 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.063 |
|
| \begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.058 |
|
| \begin{align*}
y^{\prime }-y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.066 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-x} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.112 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{{\mathrm e}^{x}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=2 \,{\mathrm e}^{-x}-x^{2} {\mathrm e}^{-x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.155 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.540 |
|