| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \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] |
✓ |
✓ |
✓ |
✗ |
113.313 |
|
| \begin{align*}
\left (y y^{\prime }+x n \right )^{2}&=\left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
13.147 |
|
| \begin{align*}
y^{2} \left (-{y^{\prime }}^{2}+1\right )&=b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.408 |
|
| \begin{align*}
\left (-y+y^{\prime } x \right ) \left (x +y y^{\prime }\right )&=h^{2} y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✗ |
✓ |
✗ |
107.954 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.918 |
|
| \begin{align*}
\left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.986 |
|
| \begin{align*}
x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.166 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.359 |
|
| \begin{align*}
{y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
0.794 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
{y^{\prime }}^{3}+m {y^{\prime }}^{2}&=a \left (y+x m \right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
27.595 |
|
| \begin{align*}
{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
69.106 |
|
| \begin{align*}
\left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
✗ |
299.332 |
|
| \begin{align*}
y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.946 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {m}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
3.312 |
|
| \begin{align*}
y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.802 |
|
| \begin{align*}
y&=y^{\prime } x +a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.253 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
\sqrt {x}\, y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
26.304 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-3 y y^{\prime } x +x^{3}+2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
2.974 |
|
| \begin{align*}
\left (1+y^{\prime }\right )^{3}&=\frac {7 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}}{4 a} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
22.099 |
|
| \begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )&=r^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.213 |
|
| \begin{align*}
x {y^{\prime }}^{2}-\left (x -a \right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.335 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.263 |
|
| \begin{align*}
a {y^{\prime }}^{3}&=27 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.934 |
|
| \begin{align*}
x {y^{\prime }}^{2}-2 y y^{\prime }+a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
3.532 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
3.532 |
|
| \begin{align*}
y^{2}-2 y y^{\prime } x +{y^{\prime }}^{2} \left (x^{2}-1\right )&=m^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✗ |
✗ |
0.731 |
|
| \begin{align*}
y&=y^{\prime } x +\sqrt {b^{2}+a^{2} y^{\prime }} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
7.642 |
|
| \begin{align*}
y&=y^{\prime } x -{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| \begin{align*}
4 {y^{\prime }}^{2}&=9 x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.498 |
|
| \begin{align*}
4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.952 |
|
| \begin{align*}
\left (8 {y^{\prime }}^{3}-27\right ) x&=12 y {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.063 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 y y^{\prime } x +y^{2}-b^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.457 |
|
| \begin{align*}
\left (-y+y^{\prime } x \right ) \left (x -y y^{\prime }\right )&=2 y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✗ |
✓ |
✗ |
102.626 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }-54 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.226 |
|
| \begin{align*}
y^{\prime \prime }-m^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.763 |
|
| \begin{align*}
2 y^{\prime \prime }+5 y^{\prime }-12 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \begin{align*}
9 y^{\prime \prime }+18 y^{\prime }-16 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.218 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.091 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.099 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-m^{2} y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.076 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{4 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
y^{\prime \prime }-y&=2+5 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.353 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-8 y^{\prime }+12 y&=X \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \begin{align*}
y^{\prime \prime \prime }+y&=3+{\mathrm e}^{-x}+5 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=\left ({\mathrm e}^{x}+1\right )^{2} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.311 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{\frac {5 x}{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.485 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x^{2} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \begin{align*}
y^{\prime \prime \prime }+8 y&=x^{4}+2 x +1 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=\cos \left (2 x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=\cos \left (a x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.917 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=2 \sin \left (\frac {x}{2}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \begin{align*}
y^{\prime \prime \prime }+y&=\sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y&=x \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.181 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| \begin{align*}
y^{\prime \prime }+2 y&=x^{2} {\mathrm e}^{3 x}+{\mathrm e}^{x} \cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.126 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=x \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.693 |
|
| \begin{align*}
y^{\prime \prime }-y&=x^{2} \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.896 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.066 |
|
| \begin{align*}
y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.113 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{2 x}+x^{2}+x \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.209 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\sin \left (3 x \right )+{\mathrm e}^{x}+x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.211 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=x +{\mathrm e}^{x m} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
y^{\prime \prime }-a^{2} y&={\mathrm e}^{a x}+{\mathrm e}^{x n} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.798 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }-6 y^{\prime }+8 y&=x \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.180 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \left (b x +a \right ) \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.249 |
|
| \begin{align*}
y^{\prime \prime \prime }-13 y^{\prime }+12 y&=x \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.176 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=\cos \left (x m \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.234 |
|
| \begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=x^{2} \cos \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=\sec \left (a x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.332 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \begin{align*}
y^{\prime \prime }+n^{2} y&={\mathrm e}^{x} x^{4} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.194 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-a^{4} y&=x^{4} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.177 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.187 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&={\mathrm e}^{x} \cos \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.159 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.501 |
|
| \begin{align*}
y^{\prime \prime \prime }-7 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (x +1\right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.190 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+4 y&={\mathrm e}^{x} \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{x} x^{2} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=x \,{\mathrm e}^{x}+{\mathrm e}^{x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.198 |
|
| \begin{align*}
y^{\prime \prime }-y&=x \sin \left (x \right )+\left (x^{2}+1\right ) {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&={\mathrm e}^{x} \cos \left (2 x \right )+\cos \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.371 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&={\mathrm e}^{x}+\cos \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
20 y-9 y^{\prime }+y^{\prime \prime }&=20 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&={\mathrm e}^{3 x} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
y^{\prime \prime \prime }+y&={\mathrm e}^{2 x} \sin \left (x \right )+{\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.946 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=2 \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.198 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y&=3 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.141 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.215 |
|
| \begin{align*}
y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.254 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=x^{4} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.830 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=x^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.179 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -20 y&=\left (x +1\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.386 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x^{5} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.676 |
|
| \begin{align*}
\left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5-2 x \right ) y^{\prime }+8 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
81.977 |
|