| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{\prime \prime }&=50 \\
x \left (0\right ) &= 20 \\
x^{\prime }\left (0\right ) &= 10 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \begin{align*}
x^{\prime \prime }&=-20 \\
x \left (0\right ) &= 5 \\
x^{\prime }\left (0\right ) &= -15 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| \begin{align*}
x^{\prime \prime }&=3 t \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.813 |
|
| \begin{align*}
x^{\prime \prime }&=2 t +1 \\
x \left (0\right ) &= 4 \\
x^{\prime }\left (0\right ) &= -7 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| \begin{align*}
x^{\prime \prime }&=4 \left (t +3\right )^{2} \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.827 |
|
| \begin{align*}
x^{\prime \prime }&=\frac {1}{\sqrt {t +4}} \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.925 |
|
| \begin{align*}
x^{\prime \prime }&=\frac {1}{\left (t +1\right )^{3}} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.909 |
|
| \begin{align*}
x^{\prime \prime }&=50 \sin \left (5 t \right ) \\
x \left (0\right ) &= 8 \\
x^{\prime }\left (0\right ) &= -10 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.953 |
|
| \begin{align*}
y^{\prime \prime } x&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=4 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x&=2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \begin{align*}
y^{\prime \prime }&=\left (x +y^{\prime }\right )^{2} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \begin{align*}
r y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.698 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.883 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.901 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.700 |
|
| \begin{align*}
2 y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.286 |
|
| \begin{align*}
2 y^{\prime \prime }-3 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.874 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.907 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \begin{align*}
2 y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| \begin{align*}
2 y^{\prime \prime }-3 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.996 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=1+t^{2}+{\mathrm e}^{-2 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| \begin{align*}
2 y^{\prime \prime }+y^{\prime }&=8 \sin \left (2 x \right )+{\mathrm e}^{-x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.811 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=x^{3} \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.812 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&={\mathrm e}^{2 x} \sin \left (x \right ) x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.589 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=x^{2} {\mathrm e}^{-x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.851 |
|
| \begin{align*}
y^{\prime \prime }&=\cos \left (t \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| \begin{align*}
y^{\prime \prime } x&=x^{2}+1 \\
\end{align*} | [[_2nd_order, _quadrature]] | ✓ | ✓ | ✓ | ✓ | 0.793 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (1+y^{\prime }\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime }+{y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.678 |
|
| \begin{align*}
y^{\prime \prime } x +x&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.975 |
|
| \begin{align*}
x^{\prime \prime }+t x^{\prime }&=t^{3} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.820 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=y^{\prime } x +1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.580 |
|
| \begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
6.421 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.974 |
|
| \begin{align*}
y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.314 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2}+y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
2.132 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.653 |
|
| \begin{align*}
y^{\prime \prime }+2 {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \begin{align*}
y^{\prime \prime }+2 {y^{\prime }}^{2}&=2 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
5.490 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&={y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.221 |
|
| \begin{align*}
y^{\prime \prime }&=\sec \left (x \right ) \tan \left (x \right ) \\
y \left (0\right ) &= \frac {\pi }{4} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.006 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \cos \left (x \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✗ |
✗ |
✗ |
0.590 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} | [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] | ✓ | ✓ | ✓ | ✓ | 0.692 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✗ |
✓ |
✗ |
0.547 |
|
| \begin{align*}
\left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }&={\mathrm e}^{x} y^{\prime } \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.354 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}+y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
6.769 |
|
| \begin{align*}
y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.573 |
|
| \begin{align*}
y^{\prime \prime }&=x^{n} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| \begin{align*}
y^{\prime \prime }&=\cos \left (x \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.842 |
|
| \begin{align*}
y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.817 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=9 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| \begin{align*}
2 y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| \begin{align*}
y^{\prime \prime } x&=x +y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&={\mathrm e}^{x} \left (x^{2}+10\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\frac {1}{{\mathrm e}^{x}+1} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.895 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| \begin{align*}
y^{\prime \prime }&=x +\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| \begin{align*}
y^{\prime \prime }&=\operatorname {c1} \cos \left (a x \right )+\operatorname {c2} \sin \left (b x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.023 |
|
| \begin{align*}
y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} | [[_2nd_order, _quadrature]] | ✓ | ✓ | ✓ | ✓ | 0.737 |
|
| \begin{align*}
y^{\prime \prime }&=\operatorname {c1} \,{\mathrm e}^{a x}+\operatorname {c2} \,{\mathrm e}^{-b x} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| \begin{align*}
\left (\csc \left (x \right )+\cot \left (x \right )\right ) y^{\prime }+y^{\prime \prime }&=1+a \csc \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
2.541 |
|
| \begin{align*}
f \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=x^{n} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.165 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
a y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \begin{align*}
-\left (-x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| \begin{align*}
-2 y^{\prime }+\left (a -x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
y^{\prime }+2 y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \begin{align*}
c y^{\prime }+\left (b x +a \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.964 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=b x +a \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| \begin{align*}
a -y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.896 |
|
| \begin{align*}
-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| \begin{align*}
a -2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.146 |
|
| \begin{align*}
4 \left (x^{2}+1\right ) y^{\prime \prime }&=x^{2}+4 y^{\prime } x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \begin{align*}
-2 a^{2} x y^{\prime }+\left (-a^{2} x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} | [[_2nd_order, _missing_y]] | ✓ | ✓ | ✓ | ✓ | 1.105 |
|
| \begin{align*}
x^{3} y^{\prime \prime }&=b x +a \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \begin{align*}
x^{3}-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.776 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.690 |
|
| \begin{align*}
y^{\prime \prime }&=2 x +\left (x^{2}-y^{\prime }\right )^{2} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
1.650 |
|
| \begin{align*}
y^{\prime \prime }&=a {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
1.224 |
|
| \begin{align*}
y^{\prime \prime }&=a^{2}+b^{2} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
10.513 |
|
| \begin{align*}
y^{\prime \prime }&={\mathrm e}^{x} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| \begin{align*}
f \left (x \right ) y^{\prime }+g \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \begin{align*}
y^{\prime }+{y^{\prime }}^{3}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.592 |
|
| \begin{align*}
y^{\prime \prime }&=\left (a -x \right ) {y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
1.563 |
|
| \begin{align*}
2 y^{\prime }+4 {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.677 |
|
| \begin{align*}
a {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
2.721 |
|
| \begin{align*}
y^{\prime \prime }&=x {y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
1.292 |
|
| \begin{align*}
y^{\prime \prime }&=a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
14.285 |
|
| \begin{align*}
y^{\prime \prime }&=a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
8.531 |
|
| \begin{align*}
y^{\prime \prime }&=a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} | [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] | ✓ | ✓ | ✓ | ✗ | 3.302 |
|
| \begin{align*}
y^{\prime \prime }&=f \left (y^{\prime }\right ) \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.925 |
|
| \begin{align*}
9 {y^{\prime }}^{4}+8 y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.326 |
|
| \begin{align*}
\left (-a \,x^{2}+2\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| \begin{align*}
x {y^{\prime }}^{2}+y^{\prime \prime } x&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
y^{\prime \prime } x&=x {y^{\prime }}^{2}+y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
-2 y^{\prime }+2 x {y^{\prime }}^{2}+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \begin{align*}
2 y^{\prime }+a \,x^{2} {y^{\prime }}^{2}+y^{\prime \prime } x&=b \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
2.900 |
|
| \begin{align*}
y^{\prime \prime } x&=y^{\prime }+{y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
1.853 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }&=a \,x^{2 k} {y^{\prime }}^{k} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
6.157 |
|
| \begin{align*}
y^{\prime }+{y^{\prime }}^{3}+2 y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
1.668 |
|
| \begin{align*}
{y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=\left (3 x -2 y^{\prime }\right ) y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.426 |
|
| \begin{align*}
2+4 y^{\prime } x +x^{2} {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.971 |
|
| \begin{align*}
-x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=-x^{2}+3 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.876 |
|
| \begin{align*}
\left (c \,x^{2}+2 b x +a \right )^{{3}/{2}} y^{\prime \prime }&=f \left (\frac {x}{\sqrt {c \,x^{2}+2 b x +a}}\right ) \\
\end{align*} | [[_2nd_order, _quadrature]] | ✓ | ✓ | ✓ | ✓ | 6.233 |
|
| \begin{align*}
y^{\prime } y^{\prime \prime }&=a^{2} x \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
4.351 |
|
| \begin{align*}
\left (x -{y^{\prime }}^{2}\right ) y^{\prime \prime }&=x^{2}-y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
110.177 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}&=a +b {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
4.185 |
|
| \begin{align*}
y^{\prime }-y^{\prime \prime } x +{y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.257 |
|
| \begin{align*}
a^{2} {y^{\prime \prime }}^{2}&=\left (1+{y^{\prime }}^{2}\right )^{3} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
24.763 |
|
| \begin{align*}
a x -2 y^{\prime } y^{\prime \prime }+x {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
0.395 |
|
| \begin{align*}
\left (-y^{\prime }+y^{\prime \prime } x \right )^{2}&=1+{y^{\prime \prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.638 |
|
| \begin{align*}
{y^{\prime \prime }}^{3}&=12 y^{\prime } \left (-2 y^{\prime }+y^{\prime \prime } x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
0.489 |
|
| \begin{align*}
f \left (y^{\prime \prime }\right )+y^{\prime \prime } x&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.252 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.846 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }&=2 \,{\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.187 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{2}+2 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x +\sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.167 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x&=1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| \begin{align*}
-y^{\prime }+y^{\prime \prime } x&=x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| \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]] | ✓ | ✓ | ✓ | ✓ | 0.566 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (1+y^{\prime }\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x&=1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.692 |
|
| \begin{align*}
-y^{\prime }+y^{\prime \prime } x&=x^{2} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.894 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right )^{3}&=a^{2} {y^{\prime \prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
21.542 |
|
| \begin{align*}
y^{\prime \prime }+9 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.859 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.820 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }&=10 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.923 |
|
| \begin{align*}
2 y^{\prime \prime }+y^{\prime }&=2 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.187 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
y^{\prime \prime } x&=y^{\prime }+{y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}&=k^{2} \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
5.678 |
|
| \begin{align*}
k&=\frac {y^{\prime \prime }}{\left (1+y^{\prime }\right )^{{3}/{2}}} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear]] |
✓ |
✓ |
✓ |
✗ |
15.774 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=4 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.816 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.188 |
|
| \begin{align*}
y^{\prime \prime }&=9 x^{2}+2 x -1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.964 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }&=-3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.129 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x&={\mathrm e}^{x} x^{3} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\
\end{align*} | [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] | ✓ | ✓ | ✓ | ✓ | 7.589 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }&=5 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.179 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
3.269 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=\frac {2}{x^{3}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| \begin{align*}
-y^{\prime }+y^{\prime \prime } x&=-\frac {2}{x}-\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| \begin{align*}
y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
1.682 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| \begin{align*}
y^{\prime \prime }&=f \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \begin{align*}
-y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.600 |
|
| \begin{align*}
u^{\prime \prime }-\cot \left (\theta \right ) u^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.185 |
|
| \begin{align*}
y^{\prime \prime }&=2+x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| \begin{align*}
y^{\prime \prime }&=1+3 x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \begin{align*}
y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.230 |
|
| \begin{align*}
-2 y^{\prime }+y^{\prime \prime } x&=x^{3} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| \begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
2.697 |
|
| \begin{align*}
y^{\prime \prime }&=-\frac {1}{2 {y^{\prime }}^{2}} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} | [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] | ✓ | ✓ | ✓ | ✓ | 5.797 |
|
| \begin{align*}
\frac {y^{\prime \prime }}{y^{\prime }}&=x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.727 |
|
| \begin{align*}
y^{\prime } y^{\prime \prime }&=x \left (x +1\right ) \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
4.947 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=2 y^{\prime } x +{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=4 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| \begin{align*}
\left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
4.282 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
3.539 |
|
| \begin{align*}
y^{\prime \prime } x&=y^{\prime }-2 {y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
1.397 |
|
| \begin{align*}
y^{\prime \prime } x -3 y^{\prime }&=5 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.861 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=12 x -10 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=10 x^{4}+2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.872 |
|
| \begin{align*}
y^{\prime \prime }&=\tan \left (x \right ) \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
3.684 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=\ln \left (x \right ) \\
y \left (1\right ) &= {\mathrm e} \\
y^{\prime }\left (1\right ) &= {\mathrm e}^{-1} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.770 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\frac {x -1}{x^{2}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.956 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.739 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.878 |
|
| \begin{align*}
t y^{\prime \prime }-y^{\prime }&=2 t^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.050 |
|
| \begin{align*}
y^{\prime \prime }&=x {y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
1.059 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x&=0 \\
y \left (2\right ) &= 5 \\
y^{\prime }\left (2\right ) &= -4 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x&=0 \\
y \left (2\right ) &= 5 \\
y^{\prime }\left (2\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
2 a y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
1.582 |
|
| \begin{align*}
y^{\prime \prime } x&=y^{\prime }+x^{5} \\
y \left (1\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.202 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+x&=0 \\
y \left (2\right ) &= -1 \\
y^{\prime }\left (2\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.277 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| \begin{align*}
y^{\prime \prime }&=x {y^{\prime }}^{2} \\
y \left (2\right ) &= \frac {\pi }{4} \\
y^{\prime }\left (2\right ) &= -{\frac {1}{4}} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.430 |
|
| \begin{align*}
y^{\prime \prime }&=x {y^{\prime }}^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
-x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=-x^{2}+3 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.722 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \begin{align*}
y^{\prime \prime }&={\mathrm e}^{x} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
2 y^{\prime \prime }&={y^{\prime }}^{3} \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
1.623 |
|
| \begin{align*}
{y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} | [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] | ✓ | ✓ | ✓ | ✓ | 3.503 |
|
| \begin{align*}
y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.457 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=y^{\prime } \left (2 x -y^{\prime }\right ) \\
y \left (-1\right ) &= 5 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=\left (3 x -2 y^{\prime }\right ) y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| \begin{align*}
y^{\prime \prime } x&=y^{\prime } \left (2-3 y^{\prime } x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.597 |
|
| \begin{align*}
x^{4} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+x^{3}\right ) \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
y^{\prime \prime }&=2 x +\left (x^{2}-y^{\prime }\right )^{2} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
1.395 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x +x^{2}&=0 \\
y \left (0\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
1.152 |
|
| \begin{align*}
y^{\prime }-y^{\prime \prime } x +{y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
{y^{\prime \prime }}^{3}&=12 y^{\prime } \left (-2 y^{\prime }+y^{\prime \prime } x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
0.670 |
|
| \begin{align*}
t y^{\prime \prime }+4 y^{\prime }&=t^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.115 |
|
| \begin{align*}
\left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime }&=0 \\
y \left (3\right ) &= 2 \pi \\
y^{\prime }\left (3\right ) &= {\frac {2}{3}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.050 |
|
| \begin{align*}
t y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-2 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.476 |
|
| \begin{align*}
y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| \begin{align*}
y^{\prime \prime }&=f \left (t \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.879 |
|
| \begin{align*}
y^{\prime \prime }&=k \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.952 |
|
| \begin{align*}
y^{\prime \prime }&=4 \sin \left (x \right )-4 \\
\end{align*} | [[_2nd_order, _quadrature]] | ✓ | ✓ | ✓ | ✓ | 1.100 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+x {y^{\prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.732 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| \begin{align*}
a y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \begin{align*}
a {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.967 |
|
| \begin{align*}
y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}&=x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.568 |
|
| \begin{align*}
{y^{\prime \prime }}^{3}&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.727 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.692 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
95.737 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
6.603 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=1 \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 59.479 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
60.365 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.513 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=x \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.777 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x +1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{2}+x +1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{3}+x^{2}+x +1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.855 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| \begin{align*}
y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.470 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.705 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.332 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x +2&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.533 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -a&=0 \\
\end{align*} | [[_2nd_order, _missing_y]] | ✓ | ✓ | ✓ | ✓ | 0.895 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (\left (a +1\right ) x +b \right ) y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.696 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (\left (\operatorname {a1} +\operatorname {b1} +1\right ) x -\operatorname {d1} \right ) y^{\prime }+\operatorname {a1} \operatorname {b1} \operatorname {d1}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.648 |
|
| \begin{align*}
\left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+2 x \left (3 x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
y^{\prime \prime }&=a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
7.387 |
|
| \begin{align*}
y^{\prime \prime }&=a \sqrt {1+{y^{\prime }}^{2}}+b \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
41.294 |
|
| \begin{align*}
y^{\prime \prime }&=a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.573 |
|
| \begin{align*}
y^{\prime \prime }-2 a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
1.132 |
|
| \begin{align*}
9 {y^{\prime }}^{4}+8 y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.560 |
|
| \begin{align*}
y^{\prime }+{y^{\prime }}^{3}+2 y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
1.295 |
|
| \begin{align*}
y^{\prime \prime }+a \,x^{n} y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| \begin{align*}
y^{\prime \prime } x +\left (a x +b \right ) y^{\prime }+c x \left (-c \,x^{2}+a x +b +1\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.991 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{2 x}+1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.852 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x&=x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} | [[_2nd_order, _quadrature]] | ✓ | ✓ | ✓ | ✓ | 1.693 |
|
| \begin{align*}
\left (y^{\prime }-y^{\prime \prime } x \right )^{2}&=1+{y^{\prime \prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.498 |
|
| \begin{align*}
y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }+2 \tan \left (x \right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✓ |
0.698 |
|
| \begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
4.412 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x&=2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.777 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.370 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
3.754 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.934 |
|
| \begin{align*}
x^{\prime \prime }&=-3 \sqrt {t} \\
x \left (1\right ) &= 4 \\
x^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
3.294 |
|
| \begin{align*}
x^{\prime }+t x^{\prime \prime }&=1 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
3.403 |
|
| \begin{align*}
\frac {x^{\prime }+t x^{\prime \prime }}{t}&=-2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.873 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }&=3 t \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.831 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }&=6+{\mathrm e}^{2 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }&=4 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
x^{\prime \prime }+\frac {x^{\prime }}{t}&=a \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }&=0 \\
y \left (0\right ) &= 13 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.947 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }&=t^{2} \\
\end{align*} | [[_2nd_order, _missing_y]] | ✓ | ✓ | ✓ | ✓ | 0.997 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }&=\tan \left (t \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.759 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.410 |
|
| \begin{align*}
u^{\prime \prime }+\frac {2 u^{\prime }}{r}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| \begin{align*}
m x^{\prime \prime }&=f \left (x^{\prime }\right ) \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.487 |
|
| \begin{align*}
{y^{\prime \prime }}^{3}+y^{\prime \prime }+1&=x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✗ |
✓ |
194.753 |
|
| \begin{align*}
y^{\prime \prime } x&=y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.400 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.360 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {1}{2 y^{\prime }} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
1.107 |
|
| \begin{align*}
-y^{\prime }+y^{\prime \prime } x&={\mathrm e}^{x} x^{2} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.163 |
|
| \begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }&=\sin \left (2 x \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}+{y^{\prime }}^{2}&=a^{2} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.499 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {1}{2 y^{\prime }} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }&=2-6 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| \begin{align*}
x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime }&=x^{2} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.973 |
|
| \begin{align*}
x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime }&=x^{2} \\
y \left (5\right ) &= 0 \\
y^{\prime }\left (5\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.009 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=3 t +2 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} | [[_2nd_order, _missing_y]] | ✓ | ✓ | ✓ | ✓ | 1.302 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=3 t +2 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {x +1}{x -1} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.980 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.284 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.334 |
|
| \begin{align*}
y^{\prime \prime }&=\sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| \begin{align*}
y^{\prime \prime }-3&=x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| \begin{align*}
y^{\prime \prime } x +2&=\sqrt {x} \\
y \left (1\right ) &= 8 \\
y^{\prime }\left (1\right ) &= 6 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.134 |
|
| \begin{align*}
y^{\prime \prime } x +4 y^{\prime }&=18 x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \begin{align*}
y^{\prime \prime } x&=2 y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=8 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| \begin{align*}
y^{\prime \prime } x&=y^{\prime }-2 x^{2} y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \begin{align*}
y^{\prime \prime }&=4 x \sqrt {y^{\prime }} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \begin{align*}
y^{\prime } y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
1.466 |
|
| \begin{align*}
y^{\prime \prime } x&=-y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| \begin{align*}
y^{\prime \prime } x -{y^{\prime }}^{2}&=6 x^{5} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.873 |
|
| \begin{align*}
y^{\prime \prime }&=2 y^{\prime }-6 \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.897 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=9 \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
y^{\prime \prime }&=4 x \sqrt {y^{\prime }} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
y^{\prime } y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
1.435 |
|
| \begin{align*}
y^{\prime \prime } x&=-y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
-y^{\prime }+y^{\prime \prime } x&=6 x^{5} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.860 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=9 \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \left (y^{\prime }-2\right ) \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
1.263 |
|
| \begin{align*}
y^{\prime \prime } x +4 y^{\prime }&=18 x^{2} \\
y \left (1\right ) &= 8 \\
y^{\prime }\left (1\right ) &= -3 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.204 |
|
| \begin{align*}
y^{\prime \prime } x&=2 y^{\prime } \\
y \left (-1\right ) &= 4 \\
y^{\prime }\left (-1\right ) &= 12 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.887 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=8 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.216 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }&=6 \\
y \left (1\right ) &= 4 \\
y^{\prime }\left (1\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.054 |
|
| \begin{align*}
2 x y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{2} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= \sqrt {3} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| \begin{align*}
y^{\prime \prime }&=-2 x {y^{\prime }}^{2} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
y^{\prime \prime }&=-2 x {y^{\prime }}^{2} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} | [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] | ✓ | ✓ | ✓ | ✗ | 0.264 |
|
| \begin{align*}
y^{\prime \prime }&=-2 x {y^{\prime }}^{2} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
0.332 |
|
| \begin{align*}
y^{\prime \prime }&=-2 x {y^{\prime }}^{2} \\
y \left (1\right ) &= -{\frac {1}{4}} \\
y^{\prime }\left (1\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{\frac {x}{2}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.088 |
|
| \begin{align*}
y^{\prime \prime }&=6 \,{\mathrm e}^{x} \sin \left (x \right ) x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=20 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.874 |
|
| \begin{align*}
y^{\prime }+2 y^{\prime \prime } x&=\sqrt {x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.858 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
2 y^{\prime \prime }-7 y^{\prime }+3&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| \begin{align*}
y^{\prime \prime } x&=3 y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \begin{align*}
-y^{\prime }+y^{\prime \prime } x&=-3 x {y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \begin{align*}
y^{\prime \prime }+9 y^{\prime }&=0 \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.818 |
|
| \begin{align*}
y^{\prime \prime }+9 y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.954 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.145 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.151 |
|
| \begin{align*}
3 y^{\prime \prime }-y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.316 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=3-4 t \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.148 |
|
| \begin{align*}
y^{\prime \prime }&=3 t^{4}-2 t \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=52 \sin \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.255 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.307 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }&=t^{2}-{\mathrm e}^{3 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.230 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=-24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.287 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }&=t^{2}-{\mathrm e}^{3 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.133 |
|
| \begin{align*}
y^{\prime \prime }&=t^{2}+{\mathrm e}^{t}+\sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.508 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=18 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.388 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }&=-{\mathrm e}^{3 t}-2 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {8}{9}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.467 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&=-3 t -4 \,{\mathrm e}^{2 t} t^{2} \\
y \left (0\right ) &= -{\frac {7}{2}} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.539 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=2 t^{2} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= {\frac {3}{2}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.304 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=-24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.585 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }&={\mathrm e}^{-3 t}-{\mathrm e}^{3 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} | [[_2nd_order, _missing_y]] | ✓ | ✓ | ✓ | ✗ | 1.914 |
|
| \begin{align*}
y^{\prime \prime }+16 y^{\prime }&=t \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.126 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }&=5 t^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.153 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }&=-3 \sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.246 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=\frac {1}{1+{\mathrm e}^{2 t}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.537 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| \begin{align*}
y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
2.301 |
|
| \begin{align*}
y^{\prime \prime } \left (2+x \right )^{5}&=1 \\
y \left (-1\right ) &= {\frac {1}{12}} \\
y^{\prime }\left (-1\right ) &= -{\frac {1}{4}} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.092 |
|
| \begin{align*}
y^{\prime \prime }&=2 x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.892 |
|
| \begin{align*}
y^{\prime \prime } x&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
y^{\prime \prime } x&=\left (2 x^{2}+1\right ) y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| \begin{align*}
y^{\prime \prime } x&=y^{\prime }+x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.873 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
2 y^{\prime \prime }&=\frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }} \\
y \left (1\right ) &= \frac {\sqrt {2}}{5} \\
y^{\prime }\left (1\right ) &= \frac {\sqrt {2}}{2} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \begin{align*}
y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
1.851 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} | [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] | ✓ | ✓ | ✓ | ✓ | 0.388 |
|
| \begin{align*}
y^{\prime \prime }&=\sqrt {1-{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.930 |
|
| \begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
3.475 |
|
| \begin{align*}
y^{\prime \prime }&=\sqrt {1+y^{\prime }} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \ln \left (y^{\prime }\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
✗ |
0.591 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+2&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.970 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \left (1+y^{\prime }\right ) \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
1.151 |
|
| \begin{align*}
3 y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
2.369 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }&=\left (x -1\right )^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| \begin{align*}
y^{\prime \prime }+7 y^{\prime }&={\mathrm e}^{-7 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.864 |
|
| \begin{align*}
4 y^{\prime \prime }-3 y^{\prime }&=x \,{\mathrm e}^{\frac {3 x}{4}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }&={\mathrm e}^{4 x} x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=-2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }&=8 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| \begin{align*}
7 y^{\prime \prime }-y^{\prime }&=14 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=3 x \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.965 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&={\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} | [[_2nd_order, _missing_y]] | ✓ | ✓ | ✓ | ✓ | 1.063 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=4 \,{\mathrm e}^{x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.281 |
|
| \begin{align*}
4 y^{\prime \prime }+8 y^{\prime }&=x \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.215 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=x +{\mathrm e}^{-4 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }&=2 \cos \left (4 x \right )^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.274 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }&=18 x -10 \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.165 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.420 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.385 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }&=1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+1&=3 \sin \left (2 x \right )+\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.727 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&=-5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \\
y \left (0\right ) &= -4 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.661 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\frac {1}{{\mathrm e}^{x}+1} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.164 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&={\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.504 |
|
| \begin{align*}
y^{\prime \prime } x -\left (2 x^{2}+1\right ) y^{\prime }&=4 x^{3} {\mathrm e}^{x^{2}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.791 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime \prime }-y^{\prime }&=\ln \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.490 |
|
| \begin{align*}
y^{\prime \prime } x +\left (2 x -1\right ) y^{\prime }&=-4 x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.571 |
|
| \begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }&=\cot \left (x \right ) \cos \left (x \right ) \\
\end{align*} | [[_2nd_order, _missing_y]] | ✓ | ✓ | ✓ | ✓ | 0.485 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=\frac {1}{x^{2}+1} \\
y \left (\infty \right ) &= \frac {\pi ^{2}}{8} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✓ |
0.973 |
|
| \begin{align*}
y^{\prime \prime }+\alpha y^{\prime }&=0 \\
y \left (0\right ) &= {\mathrm e}^{\alpha } \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.238 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=3+4 \sin \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.059 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=2 t^{4}+t^{2} {\mathrm e}^{-3 t}+\sin \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| \begin{align*}
y^{\prime \prime }&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.660 |
|
| \begin{align*}
a^{2} y^{\prime \prime }&=2 x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✗ |
✓ |
✗ |
2.365 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}+2 y^{\prime \prime } x -y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.381 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-2 y^{\prime \prime } x -y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.765 |
|
| \begin{align*}
y^{\prime \prime } x&=y^{\prime }+{y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
3.890 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=2 y^{\prime } x +{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=4 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.628 |
|
| \begin{align*}
\left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
125.749 |
|
| \begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
22.488 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} | [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] | ✓ | ✓ | ✓ | ✗ | 19.247 |
|
| \begin{align*}
y^{\prime \prime }+2 x {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x&=1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.137 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=\left (3 x -2 y^{\prime }\right ) y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| \begin{align*}
{y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
1.045 |
|
| \begin{align*}
-y^{\prime }+y^{\prime \prime } x&=3 x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.462 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.427 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=6 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.318 |
|
| \begin{align*}
y^{\prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.755 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=6 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.378 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= {\mathrm e}^{-2} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.308 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
2.023 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.735 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=12 x -10 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.761 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=10 x^{4}+2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| \begin{align*}
x^{\prime \prime }+3 x^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.476 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {m \sqrt {1+{y^{\prime }}^{2}}}{k} \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✗ | 13.754 |
|
| \begin{align*}
y^{\prime \prime }&=c \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
46.246 |
|
| \begin{align*}
y^{\prime \prime }&=c \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
25.940 |
|
| \begin{align*}
1+{y^{\prime }}^{2}+\frac {m y^{\prime \prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
28.941 |
|
| \begin{align*}
v^{\prime \prime }+\frac {2 v^{\prime }}{r}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.045 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=r y^{\prime \prime } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
27.838 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
e y^{\prime \prime }&=\frac {P \left (\frac {L}{2}-x \right )}{2} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.859 |
|
| \begin{align*}
e y^{\prime \prime }&=\frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.750 |
|
| \begin{align*}
e y^{\prime \prime }&=-\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.721 |
|
| \begin{align*}
e y^{\prime \prime }&=-P \left (L -x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.027 |
|
| \begin{align*}
e y^{\prime \prime }&=-P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.576 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }&=2 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.771 |
|
| \begin{align*}
y^{\prime \prime }&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.811 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.509 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.528 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }&=3 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.672 |
|
| \begin{align*}
x&=y^{\prime \prime }+y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.661 |
|
| \begin{align*}
V^{\prime \prime }+\frac {2 V^{\prime }}{r}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.184 |
|
| \begin{align*}
V^{\prime \prime }+\frac {V^{\prime }}{r}&=0 \\
\end{align*} | [[_2nd_order, _missing_y]] | ✓ | ✓ | ✓ | ✓ | 0.903 |
|
| \begin{align*}
v^{\prime \prime }+\frac {2 v^{\prime }}{r}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| \begin{align*}
y^{\prime \prime }&=x^{2} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \begin{align*}
y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
1.534 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
y^{\prime \prime }-a {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
2 y^{\prime }+4 {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.237 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.719 |
|
| \begin{align*}
a y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.485 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.902 |
|
| \begin{align*}
y^{\prime }+{y^{\prime }}^{3}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.148 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x&=2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {a}{x} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
a y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
y^{\prime \prime }&=a^{2}+k^{2} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
5.138 |
|
| \begin{align*}
a^{2} {y^{\prime \prime }}^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 4.175 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{r}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.975 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }&=\left (2 x +3\right ) \left (4+2 x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \begin{align*}
y^{\prime \prime }&=x +\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| \begin{align*}
y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.867 |
|
| \begin{align*}
\cos \left (x \right )^{2} y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {a}{x} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.031 |
|
| \begin{align*}
y^{\prime \prime } \sqrt {a^{2}+x^{2}}&=x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \begin{align*}
y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.233 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.080 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +a x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=a x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.973 |
|
| \begin{align*}
y^{\prime \prime } x +x {y^{\prime }}^{2}-y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
y^{\prime }-y^{\prime \prime } x -\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=x \\
\end{align*} | [[_2nd_order, _missing_y]] | ✓ | ✓ | ✓ | ✓ | 0.903 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.055 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
2.522 |
|
| \begin{align*}
y^{\prime \prime }&=a {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| \begin{align*}
a y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.106 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
3.480 |
|
| \begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
6.609 |
|
| \begin{align*}
a y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.223 |
|
| \begin{align*}
y^{\prime \prime }&=a^{2}+k^{2} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
7.435 |
|
| \begin{align*}
a^{2} {y^{\prime \prime }}^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
7.900 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
9.059 |
|
| \begin{align*}
-a y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
16.873 |
|
| \begin{align*}
{\mathrm e}^{x} \left (-y^{\prime }+y^{\prime \prime } x \right )&=x^{3} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x&=2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \begin{align*}
y^{\prime \prime }&=x^{2} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.343 |
|
| \begin{align*}
y^{\prime \prime }&=\sec \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.599 |
|
| \begin{align*}
y^{\prime }+{y^{\prime }}^{3}+y^{\prime \prime }&=0 \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 7.547 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.952 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=3 x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| \begin{align*}
x^{\prime \prime }+p x^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.922 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }&=t \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.126 |
|
| \begin{align*}
x^{\prime \prime }-\frac {x^{\prime }}{t}&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.865 |
|
| \begin{align*}
u^{\prime \prime }+\left (\tan \left (x \right )-2 \cos \left (x \right )\right ) u^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| \begin{align*}
x^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.289 |
|
| \begin{align*}
y^{\prime \prime }&=9 x^{2}+2 x -1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.577 |
|
| \begin{align*}
-y^{\prime }+y^{\prime \prime } x&=3 x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.268 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.867 |
|
| \begin{align*}
y^{\prime \prime }&=\cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.504 |
|
| \begin{align*}
\left (2+x \right ) y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
2.981 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.136 |
|
| \begin{align*}
{y^{\prime \prime }}^{2} x^{2} \left (x^{2}-1\right )-1&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.686 |
|
| \begin{align*}
y^{\prime \prime } x -{y^{\prime }}^{3}-y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
3.703 |
|
| \begin{align*}
y^{\prime }&=y^{\prime \prime } x +{y^{\prime \prime }}^{2} \\
y \left (-1\right ) &= 0 \\
y^{\prime }\left (-1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.720 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=0 \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 2.158 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&=6 x^{5} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.545 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.680 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=16 x^{3} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.806 |
|
| \begin{align*}
t y^{\prime \prime }+t^{2} y^{\prime }-\sin \left (t \right ) \sqrt {t}&=t^{2}-t +1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
3.025 |
|
| \begin{align*}
t^{2} s^{\prime \prime }-t s^{\prime }&=1-\sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.211 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
y^{\prime \prime }&=9 x^{2}+2 x -1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \begin{align*}
x^{\prime \prime }&=t^{2}-4 t +8 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \begin{align*}
y^{\prime \prime }&=1-\cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| \begin{align*}
y^{\prime \prime }+x {y^{\prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.869 |
|
| \begin{align*}
y^{\prime \prime } x -3 y^{\prime }&=4 x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.877 |
|
| \begin{align*}
y^{\prime \prime }&=2 x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 10 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| \begin{align*}
i^{\prime \prime }&=t^{2}+1 \\
i \left (0\right ) &= 2 \\
i^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.106 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=x^{2}+1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
y^{\prime } y^{\prime \prime }&=1 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
2.173 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} | [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] | ✓ | ✓ | ✓ | ✗ | 5.418 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x&=x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \begin{align*}
y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
4.728 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime }+2 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.082 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.722 |
|
| \begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{r}&=4-4 r \\
u \left (1\right ) &= 15 \\
u^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.729 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{2}+3 x +{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.830 |
|
| \begin{align*}
s^{\prime \prime }+s^{\prime }&=t +{\mathrm e}^{-t} \\
s \left (0\right ) &= 0 \\
s^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=4 x^{3}-2 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.858 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x&=5 \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.389 |
|
| \begin{align*}
T^{\prime \prime }+{T^{\prime }}^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| \begin{align*}
y^{\prime \prime } {y^{\prime }}^{2}-x^{2}&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
1.661 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.287 |
|
| \begin{align*}
x^{\prime \prime }+3 x^{\prime }&={\mathrm e}^{-3 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }&=7 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| \begin{align*}
z^{\prime \prime }+2 z^{\prime }&=3 \sin \left (x \right ) \\
\end{align*} | [[_2nd_order, _missing_y]] | ✓ | ✓ | ✓ | ✓ | 0.927 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }&=2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.903 |
|
| \begin{align*}
m s^{\prime \prime }&=\frac {g \,t^{2}}{2} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.865 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.955 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=3 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.838 |
|
| \begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
4.238 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }-2&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \begin{align*}
y^{\prime \prime }&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.816 |
|
| \begin{align*}
y^{\prime \prime }&=3 x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \begin{align*}
y^{\prime \prime } x +4 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.624 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.865 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.165 |
|
| \begin{align*}
y^{\prime \prime }&=3 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.420 |
|
| \begin{align*}
y^{\prime \prime } x&=x^{2}+1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.306 |
|
| \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]] | ✓ | ✓ | ✓ | ✓ | 0.433 |
|
| \begin{align*}
\left (2+x \right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.352 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=2 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.492 |
|
| \begin{align*}
y^{\prime \prime } x +x {y^{\prime }}^{2}-y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.399 |
|
| \begin{align*}
y^{\prime \prime }&=x {y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.614 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x +{\mathrm e}^{-x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.928 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.091 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=-\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=-18 x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=-2 x +2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.659 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&=42 \,{\mathrm e}^{4 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.716 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=2 x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| \begin{align*}
y^{\prime \prime }&=x {y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x&=0 \\
y \left (2\right ) &= 5 \\
y^{\prime }\left (2\right ) &= -4 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x&=0 \\
y \left (2\right ) &= 5 \\
y^{\prime }\left (2\right ) &= 2 \\
\end{align*} | [[_2nd_order, _missing_y]] | ✓ | ✓ | ✓ | ✓ | 0.318 |
|
| \begin{align*}
2 a y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \begin{align*}
y^{\prime \prime } x&=y^{\prime }+x^{5} \\
y \left (1\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+x&=0 \\
y \left (2\right ) &= -1 \\
y^{\prime }\left (2\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.653 |
|
| \begin{align*}
y^{\prime \prime }-x {y^{\prime }}^{2}&=0 \\
y \left (2\right ) &= \frac {\pi }{4} \\
y^{\prime }\left (2\right ) &= -{\frac {1}{4}} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.285 |
|
| \begin{align*}
y^{\prime \prime }-x {y^{\prime }}^{2}&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
-x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=-x^{2}+3 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.538 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.354 |
|
| \begin{align*}
y^{\prime \prime }&={\mathrm e}^{x} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.242 |
|
| \begin{align*}
2 y^{\prime \prime }&={y^{\prime }}^{3} \sin \left (2 x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
0.436 |
|
| \begin{align*}
{y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.224 |
|
| \begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
2.785 |
|
| \begin{align*}
y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
2.005 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=y^{\prime } \left (2 x -y^{\prime }\right ) \\
y \left (-1\right ) &= 5 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=\left (3 x -2 y^{\prime }\right ) y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \begin{align*}
y^{\prime \prime } x&=y^{\prime } \left (2-3 y^{\prime } x \right ) \\
\end{align*} | [[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] | ✓ | ✓ | ✓ | ✓ | 0.441 |
|
| \begin{align*}
x^{4} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+x^{3}\right ) \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \begin{align*}
y^{\prime \prime }&=2 x +\left (x^{2}-y^{\prime }\right )^{2} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.871 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x +x^{2}&=0 \\
y \left (0\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
0.741 |
|
| \begin{align*}
y^{\prime }-y^{\prime \prime } x +{y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.262 |
|
| \begin{align*}
{y^{\prime \prime }}^{3}&=12 y^{\prime } \left (-2 y^{\prime }+y^{\prime \prime } x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
0.502 |
|
| \begin{align*}
y^{\prime \prime }&=2 t +1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| \begin{align*}
y^{\prime \prime }&=6 \sin \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| \begin{align*}
y^{\prime \prime }&=6 \sin \left (3 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.062 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.863 |
|
| \begin{align*}
y^{\prime \prime }+2&=\cos \left (t \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-2 t y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{-3 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.881 |
|
| \begin{align*}
t y^{\prime \prime }-y^{\prime }&=3 t^{2}-1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| \begin{align*}
2 t y^{\prime \prime }-y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
y^{\prime \prime }&=f \left (t \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
y^{\prime \prime }&={\mathrm e}^{i \omega t} \\
\end{align*} | [[_2nd_order, _quadrature]] | ✓ | ✓ | ✓ | ✓ | 0.599 |
|
| \begin{align*}
y^{\prime \prime }&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| \begin{align*}
y^{\prime \prime }&=\operatorname {Direct}_{t} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.752 |
|
| \begin{align*}
y^{\prime \prime }&=4 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=t +1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=t^{2}+1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&={\mathrm e}^{2 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.798 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&={\mathrm e}^{-4 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| \begin{align*}
y^{\prime \prime }&=t \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| \begin{align*}
y^{\prime \prime }&=t^{2} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.690 |
|
| \begin{align*}
y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
1.716 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \begin{align*}
-y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.970 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.969 |
|