| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.139 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
10.061 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.661 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime }+3 x y^{\prime \prime }+2 y^{\prime }&=x \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \begin{align*}
y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=4 x \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y&=x^{2}+3 x -4 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y&=\left (x +1\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.321 |
|
| \begin{align*}
-8 y+7 x y^{\prime }-3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{2}+\frac {1}{x^{2}} \\
\end{align*} |
[[_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-x y^{\prime }+y&=\ln \left (x \right )+x \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.508 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+2 y&=x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
13.316 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y&=x^{2} \sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
64.819 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=x \ln \left (x \right ) \\
\end{align*} |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.353 |
|
| \begin{align*}
y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=\left (1+\ln \left (x \right )\right )^{2} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
2.167 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }&=\left (2 x +3\right ) \left (2 x +4\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| \begin{align*}
x y^{\prime \prime }+2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.878 |
|
| \begin{align*}
y^{\prime \prime }+{\mathrm e}^{x} \left (y^{\prime }+y\right )&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.585 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.789 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y&=x^{2}+3 x -4 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
✓ |
✓ |
✗ |
0.366 |
|
| \begin{align*}
y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x}&=x^{2} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.562 |
|
| \begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.851 |
|
| \begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.793 |
|
| \begin{align*}
y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=2 x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
5.128 |
|
| \begin{align*}
\left (2 x^{2}+3 x \right ) y^{\prime \prime }+\left (3+6 x \right ) y^{\prime }+2 y&={\mathrm e}^{x} \left (x +1\right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.941 |
|
| \begin{align*}
y y^{\prime }+{y^{\prime }}^{2} x +x y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.970 |
|
| \begin{align*}
\left (-b \,x^{2}+a x \right ) y^{\prime \prime }+2 a y^{\prime }+2 b y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.107 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 y \sin \left (x \right )&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.888 |
|
| \begin{align*}
3 y x +y^{\prime } \left (x^{2}+2\right )+4 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=2 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
0.052 |
|
| \begin{align*}
x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+x y^{\prime }+y&=\ln \left (x \right ) \\
\end{align*} |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
0.784 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+3 x^{2} y&=2 x \\
\end{align*} |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.535 |
|
| \begin{align*}
x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y&=x^{4}+2 x -5 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.665 |
|
| \begin{align*}
y^{\prime \prime \prime }&=f \left (x \right ) \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \begin{align*}
y^{2}+\left (2 y x -1\right ) y^{\prime }+x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.054 |
|
| \begin{align*}
y^{\prime \prime }&=x +\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| \begin{align*}
y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| \begin{align*}
\cos \left (x \right )^{2} y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.831 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }&=1 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {a}{x} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| \begin{align*}
y^{\prime \prime \prime } \csc \left (x \right )^{2}&=1 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.245 |
|
| \begin{align*}
y^{\prime \prime } \sqrt {a^{2}+x^{2}}&=x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \begin{align*}
y^{\prime \prime }&=y \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.756 |
|
| \begin{align*}
y^{3} y^{\prime \prime }&=a \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
3.138 |
|
| \begin{align*}
-a^{2} y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.553 |
|
| \begin{align*}
y^{\prime \prime }+\frac {a^{2}}{y}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
1.516 |
|
| \begin{align*}
y^{\prime \prime }&=y^{3}-y \\
\end{align*} |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
4.016 |
|
| \begin{align*}
y^{\prime \prime }&={\mathrm e}^{2 y} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
6.688 |
|
| \begin{align*}
y^{\prime \prime }&=x y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| \begin{align*}
y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.031 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.933 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime }-4 x y^{\prime \prime }+6 y^{\prime }&=4 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.300 |
|
| \begin{align*}
y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x \left (a^{2}-x^{2}\right )}&=\frac {x^{2}}{a \left (a^{2}-x^{2}\right )} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.313 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+a x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.864 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }&=a x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.381 |
|
| \begin{align*}
x y^{\prime \prime }+{y^{\prime }}^{2} x -y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \begin{align*}
x y^{\prime \prime \prime }-x y^{\prime \prime }-y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.287 |
|
| \begin{align*}
y^{\prime }-x y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }&=x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.139 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.394 |
|
| \begin{align*}
y y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.286 |
|
| \begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
3.509 |
|
| \begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.784 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+4 {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| \begin{align*}
y^{\prime \prime }&=a {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| \begin{align*}
1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
2.597 |
|
| \begin{align*}
y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}}&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
✗ |
44.277 |
|
| \begin{align*}
a y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.389 |
|
| \begin{align*}
a^{2} y^{\prime \prime } y^{\prime }&=x \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
4.093 |
|
| \begin{align*}
y^{\prime \prime } y^{\prime \prime \prime }&=2 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
1.030 |
|
| \begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
3.326 |
|
| \begin{align*}
a y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.483 |
|
| \begin{align*}
y^{\prime \prime }&=a^{2}+k^{2} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
5.499 |
|
| \begin{align*}
a^{2} {y^{\prime \prime }}^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
6.729 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
4.518 |
|
| \begin{align*}
a^{2} y^{\prime \prime \prime \prime }&=y^{\prime \prime } \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.063 |
|
| \begin{align*}
a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.062 |
|
| \begin{align*}
y^{\left (5\right )}-n^{2} y^{\prime \prime \prime }&={\mathrm e}^{a x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.146 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime \prime }+a^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.657 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime \prime }&=\lambda y^{\prime \prime } \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.563 |
|
| \begin{align*}
n \,x^{3} y^{\prime \prime \prime }&=-x y^{\prime }+y \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.159 |
|
| \begin{align*}
{y^{\prime }}^{2} x +x y y^{\prime \prime }&=3 y y^{\prime } \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.776 |
|
| \begin{align*}
2 x^{2} y y^{\prime \prime }+y^{2}&={y^{\prime }}^{2} x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.965 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=\sqrt {m \,x^{2} {y^{\prime }}^{3}+n y^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
2.374 |
|
| \begin{align*}
x^{4} y^{\prime \prime }&=\left (x^{3}+2 y x \right ) y^{\prime }-4 y^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
4.647 |
|
| \begin{align*}
x^{4} y^{\prime \prime }-x^{3} y^{\prime }&={y^{\prime }}^{2} x^{2}-4 y^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
5.927 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{2}-6 y&=x^{4} {y^{\prime }}^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.984 |
|
| \begin{align*}
y^{\prime \prime }&={\mathrm e}^{y} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
10.258 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.928 |
|
| \begin{align*}
a y^{\prime \prime \prime }&=y^{\prime \prime } \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime \prime }+1&=0 \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| \begin{align*}
y^{\prime \prime \prime }&=\sin \left (x \right )^{2} \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.184 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {1}{\sqrt {a y}} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
24.520 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.778 |
|
| \begin{align*}
-a y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
12.320 |
|
| \begin{align*}
\sin \left (y\right )^{3} y^{\prime \prime }&=\cos \left (y\right ) \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
98.262 |
|
| \begin{align*}
{\mathrm e}^{x} \left (-y^{\prime }+x y^{\prime \prime }\right )&=x^{3} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }&=2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| \begin{align*}
2 x y^{\prime \prime } y^{\prime \prime \prime }&=-a^{2}+{y^{\prime \prime }}^{2} \\
\end{align*} |
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
2.034 |
|