| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=-5 x-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
x^{\prime }&=11 x-2 y \\
y^{\prime }&=3 x+4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.462 |
|
| \begin{align*}
x^{\prime }&=x+20 y \\
y^{\prime }&=40 x-19 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
x^{\prime }&=-2 x+2 y \\
y^{\prime }&=x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| \begin{align*}
x^{\prime }&=-2 x+3 y \\
y^{\prime }&=-6 x+4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| \begin{align*}
x^{\prime }&=-11 x-2 y \\
y^{\prime }&=13 x-9 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
x^{\prime }&=7 x-5 y \\
y^{\prime }&=10 x-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.600 |
|
| \begin{align*}
x^{\prime }&=5 x-4 y \\
y^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \begin{align*}
x^{\prime }&=-6 x+2 y \\
y^{\prime }&=-2 x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
x^{\prime }&=-3 x-y \\
y^{\prime }&=x-5 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
x^{\prime }&=13 x \\
y^{\prime }&=13 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.289 |
|
| \begin{align*}
x^{\prime }&=7 x-4 y \\
y^{\prime }&=x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
\tan \left (y\right )-\cot \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.562 |
|
| \begin{align*}
12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
30.263 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.355 |
|
| \begin{align*}
y^{\prime } x +y&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.862 |
|
| \begin{align*}
y-y^{\prime } x&=x^{2} y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.133 |
|
| \begin{align*}
x^{\prime }+3 x&={\mathrm e}^{2 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.667 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.122 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.423 |
|
| \begin{align*}
x^{\prime }&=x+\sin \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.935 |
|
| \begin{align*}
x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.381 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.624 |
|
| \begin{align*}
{y^{\prime }}^{2}&=9 y^{4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{\frac {x}{t}}+\frac {x}{t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.505 |
|
| \begin{align*}
{y^{\prime }}^{2}+x^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {1}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.246 |
|
| \begin{align*}
x&={y^{\prime }}^{3}-y^{\prime }+2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.865 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{y^{3}+x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
5.813 |
|
| \begin{align*}
y&={y^{\prime }}^{4}-{y^{\prime }}^{3}-2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
105.360 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{2}&=4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y-x -4}{2 x -y+5} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.957 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x +1}+y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.271 |
|
| \begin{align*}
y^{\prime }&=x +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
30.754 |
|
| \begin{align*}
y^{\prime }&=x y^{3}+x^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
✗ |
7.918 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
5.768 |
|
| \begin{align*}
2 x +2 y-1+\left (x +y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.832 |
|
| \begin{align*}
{y^{\prime }}^{3}-{\mathrm e}^{2 x} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
y&=5 y^{\prime } x -{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.102 |
|
| \begin{align*}
y^{\prime }&=x -y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
42.046 |
|
| \begin{align*}
y^{\prime }&=\left (x -5 y\right )^{{1}/{3}}+2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.609 |
|
| \begin{align*}
y \left (x -y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.441 |
|
| \begin{align*}
x^{\prime }+5 x&=10 t +2 \\
x \left (1\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.646 |
|
| \begin{align*}
x^{\prime }&=\frac {x}{t}+\frac {x^{2}}{t^{3}} \\
x \left (2\right ) &= 4 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.354 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{2} \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.360 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -4 y-2}{3 x -4 y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.958 |
|
| \begin{align*}
x^{\prime }-x \cot \left (t \right )&=4 \sin \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.511 |
|
| \begin{align*}
y&=x^{2}+2 y^{\prime } x +\frac {{y^{\prime }}^{2}}{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✗ |
✓ |
2.172 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}+x^{3} y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.445 |
|
| \begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| \begin{align*}
x^{2}-y+\left (y^{2} x^{2}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.131 |
|
| \begin{align*}
3 y^{2}-x +2 y \left (y^{2}-3 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
13.143 |
|
| \begin{align*}
y \left (x -y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.512 |
|
| \begin{align*}
y^{\prime }&=\frac {-3+x +y}{y-x +1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.053 |
|
| \begin{align*}
y^{\prime } x -y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.883 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.931 |
|
| \begin{align*}
\left (3+2 x +4 y\right ) y^{\prime }-2 y-x -1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.630 |
|
| \begin{align*}
\left (y^{2}-x \right ) y^{\prime }-y+x^{2}&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.099 |
|
| \begin{align*}
\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.854 |
|
| \begin{align*}
3 y^{2} y^{\prime } x +y^{3}-2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.432 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (a +x \right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.208 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.468 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+10 y&=100 \\
y \left (0\right ) &= 10 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \begin{align*}
x^{\prime \prime }+x&=\sin \left (t \right )-\cos \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.824 |
|
| \begin{align*}
y^{\prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.138 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {1}{\sin \left (x \right )^{3}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.336 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cosh \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 {y^{\prime }}^{2}}{1-y}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.369 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }+4 x&={\mathrm e}^{t}+{\mathrm e}^{2 t}+1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.568 |
|
| \begin{align*}
x^{3} x^{\prime \prime }+1&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
3.395 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-16 y&=x^{2}-{\mathrm e}^{x} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| \begin{align*}
{y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2}&=1 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✓ |
✗ |
1.401 |
|
| \begin{align*}
x^{\left (6\right )}-x^{\prime \prime \prime \prime }&=1 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.215 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }-2 x^{\prime \prime }+x&=t^{2}-3 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.216 |
|
| \begin{align*}
y^{\prime \prime }+4 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-\frac {1}{25}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.447 |
|
| \begin{align*}
y^{\prime \prime }&=3 \sqrt {y} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
11.217 |
|
| \begin{align*}
y^{\prime \prime }+y&=1-\frac {1}{\sin \left (x \right )} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
u^{\prime \prime }+\frac {2 u^{\prime }}{r}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=\frac {y y^{\prime }}{\sqrt {x^{2}+1}} \\
\end{align*} |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.721 |
|
| \begin{align*}
y y^{\prime } y^{\prime \prime }&={y^{\prime }}^{3}+{y^{\prime \prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.875 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=t \sin \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\sinh \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.615 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&={\mathrm e}^{x} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.174 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=x \,{\mathrm e}^{x} \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-6 y&=1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.424 |
|
| \begin{align*}
m x^{\prime \prime }&=f \left (x\right ) \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
2.671 |
|
| \begin{align*}
m x^{\prime \prime }&=f \left (x^{\prime }\right ) \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| \begin{align*}
y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }&=x \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.242 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x&=\cos \left (t \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=2 \cos \left (\ln \left (x +1\right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
6.727 |
|
| \begin{align*}
x^{3} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.170 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }+x&=t^{3} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.187 |
|