| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
3 {y^{\prime }}^{5}-y y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.577 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x +y^{\prime } \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.792 |
|
| \begin{align*}
{y^{\prime }}^{2} x +a x&=2 y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
1.811 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{\prime }&={\mathrm e}^{y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.104 |
|
| \begin{align*}
y&=\sin \left (y^{\prime }\right )-y^{\prime } \cos \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
12.833 |
|
| \begin{align*}
y&=\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.727 |
|
| \begin{align*}
y&=\ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.243 |
|
| \begin{align*}
x&=y y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.518 |
|
| \begin{align*}
\left (2 x -b \right ) y^{\prime }&=y-a y {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.181 |
|
| \begin{align*}
x&=y+a \ln \left (y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.169 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.661 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.341 |
|
| \begin{align*}
x^{2}&=a^{2} \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
y&=x y^{\prime }+\frac {a}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.835 |
|
| \begin{align*}
y&=x y^{\prime }+y^{\prime }-{y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.592 |
|
| \begin{align*}
y&=x y^{\prime }+a y^{\prime } \left (1-y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
y&=x y^{\prime }+\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
3.230 |
|
| \begin{align*}
y&=x y^{\prime }+\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
5.405 |
|
| \begin{align*}
\left (-x y^{\prime }+y\right ) \left (y^{\prime }-1\right )&=y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.537 |
|
| \begin{align*}
{y^{\prime }}^{2} x -y y^{\prime }+a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.717 |
|
| \begin{align*}
y&=y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.419 |
|
| \begin{align*}
y&=x y^{\prime }+{y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.516 |
|
| \begin{align*}
4 y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.350 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.662 |
|
| \begin{align*}
x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+2 y^{2}&=x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.428 |
|
| \begin{align*}
y&=x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.855 |
|
| \begin{align*}
x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
4.361 |
|
| \begin{align*}
y&=\frac {2 a {y^{\prime }}^{2}}{\left (1+{y^{\prime }}^{2}\right )^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.546 |
|
| \begin{align*}
\left (x y^{\prime }-y\right )^{2}&=a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
168.915 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x +4 y y^{\prime }&=y^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
1.758 |
|
| \begin{align*}
2 {y^{\prime }}^{3}-\left (2 x +4 \sin \left (x \right )-\cos \left (x \right )\right ) {y^{\prime }}^{2}-\left (x \cos \left (x \right )-4 x \sin \left (x \right )+\sin \left (2 x \right )\right ) y^{\prime }+\sin \left (2 x \right ) x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.027 |
|
| \begin{align*}
\left (x y^{\prime }-y\right )^{2}&={y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
97.241 |
|
| \begin{align*}
-x y^{\prime }+y&=y y^{\prime }+x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.508 |
|
| \begin{align*}
a^{2} y {y^{\prime }}^{2}-4 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.566 |
|
| \begin{align*}
x^{2} \left (-x y^{\prime }+y\right )&=y {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.332 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
1.727 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}+a^{4}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.629 |
|
| \begin{align*}
y y^{\prime }+x&=a {y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.375 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| \begin{align*}
2 y&=x y^{\prime }+\frac {a}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.319 |
|
| \begin{align*}
y&=\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.930 |
|
| \begin{align*}
\left (a {y^{\prime }}^{2}-b \right ) x y+\left (b \,x^{2}-a y^{2}+c \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
101.198 |
|
| \begin{align*}
y&=a y^{\prime }+b {y^{\prime }}^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.502 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (y+2 x -{\mathrm e}^{x -y}\right ) {y^{\prime }}^{2}+\left (2 y x -2 x \,{\mathrm e}^{x -y}-y \,{\mathrm e}^{x -y}\right ) y^{\prime }+2 x y \,{\mathrm e}^{x -y}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \begin{align*}
\left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }&=3 x y^{2}-x^{2} \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.474 |
|
| \begin{align*}
\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}&=1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.675 |
|
| \begin{align*}
\left (x^{3} y^{3}+x^{2} y^{2}+y x +1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| \begin{align*}
\left (x \cos \left (\frac {y}{x}\right )+\sin \left (\frac {y}{x}\right ) y\right ) y&=\left (\sin \left (\frac {y}{x}\right ) y-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
21.902 |
|
| \begin{align*}
\left (x y^{\prime }-y\right ) \left (y y^{\prime }+x \right )&=h^{2} y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
75.246 |
|
| \begin{align*}
x^{2} y^{2}-3 x y y^{\prime }&=2 y^{2}+x^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
4.087 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
1.922 |
|
| \begin{align*}
y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right )&=m \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.529 |
|
| \begin{align*}
y&=x y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| \begin{align*}
4 {y^{\prime }}^{2}&=9 x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
1.453 |
|
| \begin{align*}
\left (8 {y^{\prime }}^{3}-27\right ) x&=\frac {12 {y^{\prime }}^{2}}{x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
53.995 |
|
| \begin{align*}
3 y&=2 x y^{\prime }-\frac {2 {y^{\prime }}^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
2.049 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.147 |
|
| \begin{align*}
\left (2-3 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x&=\left (3 x -1\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| \begin{align*}
{y^{\prime }}^{2} x -\left (x -a \right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.688 |
|
| \begin{align*}
y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| \begin{align*}
3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.234 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x^{3} y^{\prime }-4 x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
y^{2} \left (-x y^{\prime }+y\right )&=x^{4} {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
3.666 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.511 |
|
| \begin{align*}
{y^{\prime }}^{4}&=4 y \left (x y^{\prime }-2 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
153.132 |
|
| \begin{align*}
\left (1-y^{2}\right ) {y^{\prime }}^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.911 |
|
| \begin{align*}
x^{2}+y&={y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
15.877 |
|
| \begin{align*}
{y^{\prime }}^{3}&=y^{4} \left (x y^{\prime }+y\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.950 |
|
| \begin{align*}
\left (1-y^{\prime }\right )^{2}-{\mathrm e}^{-2 y}&={\mathrm e}^{-2 x} {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.783 |
|
| \begin{align*}
a x y {y^{\prime }}^{2}+\left (x^{2}-a y^{2}-b \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
108.727 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\left (4 y+1\right ) \left (y^{\prime }-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
9.090 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+b^{2}-y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.248 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}-1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
162.364 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}-h^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
133.563 |
|
| \begin{align*}
8 x {y^{\prime }}^{3}&=y \left (12 {y^{\prime }}^{2}-9\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.414 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x^{2} \left (x -1\right )-4 y^{\prime } x y \left (4 x -3\right )+\left (16 x -9\right ) y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| \begin{align*}
\left (x^{2} y^{\prime }+y^{2}\right ) \left (x y^{\prime }+y\right )&=\left (y^{\prime }+1\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
58.789 |
|
| \begin{align*}
-x y^{\prime }+y&=a \left (y^{\prime }+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.903 |
|
| \begin{align*}
-x y^{\prime }+y&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.685 |
|
| \begin{align*}
\left (x y^{\prime }-y\right ) \left (x -y y^{\prime }\right )&=2 y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
65.365 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.044 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=2 \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.533 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.138 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime }-2 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.274 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=\ln \left (x \right )^{2} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}}&=1 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime }+x y^{\prime \prime }-4 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.279 |
|
| \begin{align*}
-8 y+7 x y^{\prime }-3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.139 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.777 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime }+3 x y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y&=3 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y&=x^{5} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.537 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=x^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.871 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.418 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y&=x^{4} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.679 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=x^{m} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.937 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x^{m} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.505 |
|