| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }+n^{2} y&=\sec \left (n x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.957 |
|
| \begin{align*}
y^{\prime \prime \prime }+y&=\left (1+{\mathrm e}^{x}\right )^{2} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+y&=a \cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
y^{\prime \prime \prime }+a^{2} y^{\prime }&=\sin \left (a x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x^{2} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.141 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=2 \sinh \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.740 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=\cos \left (a x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.006 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \begin{align*}
x^{2} \left ({y^{\prime }}^{2}-y^{2}\right )+y^{2}&=x^{4}+2 x y y^{\prime } \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
10.946 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.010 |
|
| \begin{align*}
y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.918 |
|
| \begin{align*}
y&=\frac {x}{y^{\prime }}-a y^{\prime } \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
72.451 |
|
| \begin{align*}
{y^{\prime }}^{3}+m {y^{\prime }}^{2}&=a \left (y+m x \right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
31.217 |
|
| \begin{align*}
x {y^{\prime }}^{3}&=a +b y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.994 |
|
| \begin{align*}
y^{\prime }&=\tan \left (x -\frac {y^{\prime }}{1+{y^{\prime }}^{2}}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
1.303 |
|
| \begin{align*}
a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.901 |
|
| \begin{align*}
y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.295 |
|
| \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] |
✓ |
✓ |
✗ |
✗ |
96.226 |
|
| \begin{align*}
y&=2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.613 |
|
| \begin{align*}
y&=-x y^{\prime }+x^{4} {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.240 |
|
| \begin{align*}
y-2 x y^{\prime }+a y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.917 |
|
| \begin{align*}
x^{2} \left (-x y^{\prime }+y\right )&=y {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.572 |
|
| \begin{align*}
x y \left (-x y^{\prime }+y\right )&=y y^{\prime }+x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.948 |
|
| \begin{align*}
x y^{2} \left ({y^{\prime }}^{2}+2\right )&=2 y^{3} y^{\prime }+x^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| \begin{align*}
3 y {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2}&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
255.404 |
|
| \begin{align*}
\left (y y^{\prime }+n x \right )^{2}&=\left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
10.938 |
|
| \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’)‘] |
✗ |
✓ |
✗ |
✗ |
293.472 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) \left (y^{\prime }+1\right )^{2}-2 \left (x +y\right ) \left (y^{\prime }+1\right ) \left (y y^{\prime }+x \right )+\left (y y^{\prime }+x \right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
121.760 |
|
| \begin{align*}
\left (-x^{2}+1\right ) {y^{\prime }}^{2}&=1-y^{2} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.612 |
|
| \begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )&=r^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| \begin{align*}
\sin \left (x y^{\prime }\right ) \cos \left (y\right )&=\cos \left (x y^{\prime }\right ) \sin \left (y\right )+y^{\prime } \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.083 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x&=\left (3 x -a \right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.270 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x \left (x -a \right ) \left (x -b \right )&=\left (3 x^{2}-2 x \left (a +b \right )+a b \right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.660 |
|
| \begin{align*}
{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
0.603 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.158 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
2.789 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{3}+\left (2 x +y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
52.036 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.849 |
|
| \begin{align*}
{y^{\prime }}^{2} y^{2} \cos \left (a \right )^{2}-2 y^{\prime } x y \sin \left (a \right )^{2}+y^{2}-x^{2} \sin \left (a \right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
77.649 |
|
| \begin{align*}
\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 y x +x^{2}+2\right ) y^{\prime }+2 y^{2}+1&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✓ |
✗ |
120.121 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=1 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y&=x^{2}+\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
-2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{2}+3 x \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.162 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=2 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.528 |
|
| \begin{align*}
2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=10 x +\frac {10}{x} \\
\end{align*} |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {1}{\left (1-x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
5.227 |
|
| \begin{align*}
\left (2 x -1\right )^{3} y^{\prime \prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| \begin{align*}
6 y-4 \left (x +a \right ) y^{\prime }+\left (x +a \right )^{2} y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.832 |
|
| \begin{align*}
16 \left (x +1\right )^{4} y^{\prime \prime \prime \prime }+96 \left (x +1\right )^{3} y^{\prime \prime \prime }+104 \left (x +1\right )^{2} y^{\prime \prime }+8 \left (x +1\right ) y^{\prime }+y&=x^{2}+4 x +3 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.076 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
10.775 |
|
| \begin{align*}
2 x^{2} y y^{\prime \prime }+4 y^{2}&={y^{\prime }}^{2} x^{2}+2 x y y^{\prime } \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
2.361 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y&=n^{2} x^{m} \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.802 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+y&=\frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
30.559 |
|
| \begin{align*}
\left (x^{2}+x +1\right ) y^{\prime \prime \prime }+\left (3+6 x \right ) y^{\prime \prime }+6 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.293 |
|
| \begin{align*}
\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y&=\frac {2}{x^{3}} \\
\end{align*} |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
✓ |
✓ |
✗ |
0.362 |
|
| \begin{align*}
y^{\prime \prime \prime }+\cos \left (x \right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=\sin \left (2 x \right ) \\
\end{align*} |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
✓ |
✓ |
✗ |
0.260 |
|
| \begin{align*}
\sqrt {x}\, y^{\prime \prime }+2 x y^{\prime }+3 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
14.022 |
|
| \begin{align*}
2 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3+7 x \right ) y^{\prime }-3 y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.570 |
|
| \begin{align*}
2 x^{2} \cos \left (y\right ) y^{\prime \prime }-2 x^{2} \sin \left (y\right ) {y^{\prime }}^{2}+x \cos \left (y\right ) y^{\prime }-\sin \left (y\right )&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
30.802 |
|
| \begin{align*}
x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2}-3 y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.694 |
|
| \begin{align*}
y+3 x y^{\prime }+2 y {y^{\prime }}^{2}+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
5.251 |
|
| \begin{align*}
\left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime }+2 \left (x +y\right ) {y^{\prime }}^{2}+x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]] |
✗ |
✗ |
✗ |
✗ |
116.104 |
|
| \begin{align*}
y^{\prime \prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.110 |
|
| \begin{align*}
y^{\prime \prime }&=x^{2} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| \begin{align*}
y^{\prime \prime }&=\sec \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.158 |
|
| \begin{align*}
y^{\prime }+{y^{\prime }}^{3}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.451 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.029 |
|
| \begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
3.869 |
|
| \begin{align*}
y^{\prime }-y y^{\prime \prime }&=n \sqrt {{y^{\prime }}^{2}+a^{2} y^{\prime \prime }} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
1118.642 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.977 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-a^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.067 |
|
| \begin{align*}
x^{4} y^{\prime \prime }&=\left (-x y^{\prime }+y\right )^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
7.864 |
|
| \begin{align*}
2 y^{\prime }+x y^{\prime \prime }&=-y^{2}+x^{2} y^{\prime } \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
4.851 |
|
| \begin{align*}
x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.446 |
|
| \begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }&=2 y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.246 |
|
| \begin{align*}
-y+x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=x \left (-x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.553 |
|
| \begin{align*}
\left (x +2\right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y&={\mathrm e}^{x} \left (x +1\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.257 |
|
| \begin{align*}
y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-\left (1-\cot \left (x \right )\right ) y&={\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
17.523 |
|
| \begin{align*}
\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.188 |
|
| \begin{align*}
y^{\prime \prime }+\left (1+\frac {2 \cot \left (x \right )}{x}-\frac {2}{x^{2}}\right ) y&=x \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
✗ |
15.822 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 \left (x^{2}+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.537 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.629 |
|
| \begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✗ |
0.813 |
|
| \begin{align*}
y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y&=-3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.125 |
|
| \begin{align*}
y^{\prime \prime }-\left (8 \,{\mathrm e}^{2 x}+2\right ) y^{\prime }+4 \,{\mathrm e}^{4 x} y&={\mathrm e}^{6 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.248 |
|
| \begin{align*}
y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+\frac {\csc \left (x \right )^{2} y}{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.491 |
|
| \begin{align*}
x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.283 |
|
| \begin{align*}
x y^{\prime \prime }-y^{\prime }-4 x^{3} y&=8 x^{3} \sin \left (x^{2}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.401 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 \cos \left (x \right )^{3} y&=2 \cos \left (x \right )^{5} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
6.667 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
16.227 |
|
| \begin{align*}
x y^{\prime \prime }+\left (x -1\right ) y^{\prime }-y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.296 |
|