| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
3 {y^{\prime }}^{5}-y^{\prime } y+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.340 |
|
| \begin{align*}
y&=x {y^{\prime }}^{2}+y^{\prime } \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.305 |
|
| \begin{align*}
x {y^{\prime }}^{2}+a x&=2 y^{\prime } y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
0.632 |
|
| \begin{align*}
y^{\prime }+{y^{\prime }}^{3}&={\mathrm e}^{y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.715 |
|
| \begin{align*}
y&=\sin \left (y^{\prime }\right )-y^{\prime } \cos \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
8.832 |
|
| \begin{align*}
y&=\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.988 |
|
| \begin{align*}
y&=\ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.513 |
|
| \begin{align*}
x&=y^{\prime } y-{y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.748 |
|
| \begin{align*}
\left (2 x -b \right ) y^{\prime }&=y-a y {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.184 |
|
| \begin{align*}
x&=y+a \ln \left (y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.510 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 y^{\prime } x&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \begin{align*}
x^{2}&=a^{2} \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {a}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.563 |
|
| \begin{align*}
y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.463 |
|
| \begin{align*}
y&=y^{\prime } x +a y^{\prime } \left (1-y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.250 |
|
| \begin{align*}
y&=y^{\prime } x +\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _rational, _Clairaut] | ✓ | ✓ | ✓ | ✗ | 1.555 |
|
| \begin{align*}
y&=y^{\prime } x +\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.719 |
|
| \begin{align*}
\left (y-y^{\prime } x \right ) \left (y^{\prime }-1\right )&=y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.259 |
|
| \begin{align*}
x {y^{\prime }}^{2}-y^{\prime } y+a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.505 |
|
| \begin{align*}
y&=y^{\prime } \left (-b +x \right )+\frac {a}{y^{\prime }} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.272 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.370 |
|
| \begin{align*}
4 y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.309 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.168 |
|
| \begin{align*}
x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-2 x y^{\prime } y+2 y^{2}&=x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.735 |
|
| \begin{align*}
y&=y^{\prime } x +x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.388 |
|
| \begin{align*}
x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
2.537 |
|
| \begin{align*}
y&=\frac {2 a {y^{\prime }}^{2}}{\left (1+{y^{\prime }}^{2}\right )^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.697 |
|
| \begin{align*}
\left (-y+y^{\prime } x \right )^{2}&=a \left (1+{y^{\prime }}^{2}\right ) \left (y^{2}+x^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
89.935 |
|
| \begin{align*}
4 x {y^{\prime }}^{2}+4 y^{\prime } y&=y^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
1.007 |
|
| \begin{align*}
2 {y^{\prime }}^{3}-\left (2 x +4 \sin \left (x \right )-\cos \left (x \right )\right ) {y^{\prime }}^{2}-\left (\cos \left (x \right ) x -4 x \sin \left (x \right )+\sin \left (2 x \right )\right ) y^{\prime }+\sin \left (2 x \right ) x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.082 |
|
| \begin{align*}
\left (-y+y^{\prime } x \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)]‘]] |
✗ |
✓ |
✓ |
✗ |
29.470 |
|
| \begin{align*}
y-y^{\prime } x&=y^{\prime } y+x \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] | ✓ | ✓ | ✓ | ✓ | 3.656 |
|
| \begin{align*}
a^{2} y {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.919 |
|
| \begin{align*}
x^{2} \left (y-y^{\prime } x \right )&=y {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.960 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
1.129 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}+a^{4}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.746 |
|
| \begin{align*}
y^{\prime } y+x&=a {y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
29.817 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \begin{align*}
2 y&=y^{\prime } x +\frac {a}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.859 |
|
| \begin{align*}
y&=\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
13.447 |
|
| \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] |
✗ |
✗ |
✓ |
✗ |
67.817 |
|
| \begin{align*}
y&=a y^{\prime }+b {y^{\prime }}^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.132 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
0.295 |
|
| \begin{align*}
\left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }&=3 x y^{2}-x^{2} \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.221 |
|
| \begin{align*}
\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}&=1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.317 |
|
| \begin{align*}
\left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
6.999 |
|
| \begin{align*}
\left (-y+y^{\prime } x \right ) \left (y^{\prime } y+x \right )&=h^{2} y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✗ |
✓ |
✗ |
154.206 |
|
| \begin{align*}
y^{2} x^{2}-3 x y^{\prime } y&=2 y^{2}+x^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
3.216 |
|
| \begin{align*}
x {y^{\prime }}^{2}-2 y^{\prime } y+a x&=0 \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, _dAlembert] | ✓ | ✓ | ✗ | ✓ | 0.704 |
|
| \begin{align*}
y^{2}-2 x y^{\prime } y+{y^{\prime }}^{2} \left (x^{2}-1\right )&=m \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.316 |
|
| \begin{align*}
y&=y^{\prime } x -{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.202 |
|
| \begin{align*}
4 {y^{\prime }}^{2}&=9 x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| \begin{align*}
\left (8 {y^{\prime }}^{3}-27\right ) x&=\frac {12 {y^{\prime }}^{2}}{x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
63.197 |
|
| \begin{align*}
3 y&=2 y^{\prime } x -\frac {2 {y^{\prime }}^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
0.852 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| \begin{align*}
\left (2-3 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
4 x {y^{\prime }}^{2}&=\left (3 x -1\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| \begin{align*}
x {y^{\prime }}^{2}-\left (x -a \right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| \begin{align*}
y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \begin{align*}
3 x {y^{\prime }}^{2}-6 y^{\prime } y+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x^{3} y^{\prime }-4 x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.241 |
|
| \begin{align*}
y^{2} \left (y-y^{\prime } x \right )&=x^{4} {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
1.268 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y^{\prime } y-x^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.294 |
|
| \begin{align*}
{y^{\prime }}^{4}&=4 y \left (y^{\prime } x -2 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
71.869 |
|
| \begin{align*}
\left (1-y^{2}\right ) {y^{\prime }}^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.822 |
|
| \begin{align*}
y+x^{2}&={y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
2.488 |
|
| \begin{align*}
{y^{\prime }}^{3}&=y^{4} \left (y^{\prime } x +y\right ) \\
\end{align*} | [[_1st_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 0.763 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.509 |
|
| \begin{align*}
a x y {y^{\prime }}^{2}+\left (x^{2}-a y^{2}-b \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_rational] |
✓ |
✗ |
✓ |
✗ |
112.175 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\left (4 y+1\right ) \left (y^{\prime }-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.993 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y^{\prime } y+b^{2}-y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.487 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}-1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✓ |
✗ |
83.497 |
|
| \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’)‘] |
✗ |
✗ |
✗ |
✗ |
14.890 |
|
| \begin{align*}
8 x {y^{\prime }}^{3}&=y \left (12 {y^{\prime }}^{2}-9\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.011 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \begin{align*}
\left (x^{2} y^{\prime }+y^{2}\right ) \left (y^{\prime } x +y\right )&=\left (1+y^{\prime }\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
32.674 |
|
| \begin{align*}
y-y^{\prime } x&=a \left (y^{\prime }+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.696 |
|
| \begin{align*}
y-y^{\prime } x&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.224 |
|
| \begin{align*}
\left (-y+y^{\prime } x \right ) \left (x -y^{\prime } y\right )&=2 y^{\prime } \\
\end{align*} |
[_rational] |
✗ |
✗ |
✓ |
✗ |
47.078 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=2 \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.548 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime }-2 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.177 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=\ln \left (x \right )^{2} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.271 |
|
| \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]] | ✓ | ✓ | ✓ | ✓ | 0.319 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime }+y^{\prime \prime } x -4 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.180 |
|
| \begin{align*}
-8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.113 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime }+3 y^{\prime \prime } x +2 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.248 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y&=3 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x^{5} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.601 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=x^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.154 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.440 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=x^{4} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.179 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{m} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.143 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{m} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.339 |
|