These are linear second order ode’s which happened to be exact. Solved by reducing them to first order ode. Number of problems in this table is 338
Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.687 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.519 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.936 |
|
|
\[ {}2 y^{\prime \prime }+3 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.956 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.293 |
|
|
\[ {}2 y^{\prime \prime }-3 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.945 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.015 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.044 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.002 |
|
|
\[ {}t^{2} y^{\prime \prime }+4 t y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.901 |
|
|
\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.383 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.599 |
|
|
\[ {}t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.947 |
|
|
\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.5 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.006 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.412 |
|
|
\[ {}\left (x^{2}-4\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.375 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 2 x^{2}+2 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.238 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = x^{\frac {3}{2}} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.704 |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 x \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
16.8 |
|
|
\[ {}\left (1+x \right ) \left (2 x +3\right ) y^{\prime \prime }+2 \left (2+x \right ) y^{\prime }-2 y = \left (2 x +3\right )^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.083 |
|
|
\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.391 |
|
|
\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
4.299 |
|
|
\[ {}y^{\prime \prime }+t y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.205 |
|
|
\[ {}y^{\prime \prime }+t y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.416 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.682 |
|
|
\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.304 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.58 |
|
|
\[ {}y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.107 |
|
|
\[ {}2 y^{\prime \prime }+y^{\prime } = 8 \sin \left (2 x \right )+{\mathrm e}^{-x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
8.673 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = x^{3} \sin \left (2 x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
19.685 |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = x \,{\mathrm e}^{2 x} \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
7.667 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{-x} \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
14.476 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 1-x \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
5.723 |
|
|
\[ {}y^{\prime \prime } = \cos \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.969 |
|
|
\[ {}x y^{\prime \prime } = x^{2}+1 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.438 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime } = y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.671 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (y^{\prime }+1\right ) = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.365 |
|
|
\[ {}x y^{\prime \prime }+x = y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
4.142 |
|
|
\[ {}y^{\prime \prime } = \sec \left (x \right ) \tan \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
3.814 |
|
|
\[ {}\left (-{\mathrm e}^{x}+1\right ) y^{\prime \prime } = {\mathrm e}^{x} y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.575 |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }+3 \left (1+x \right ) y^{\prime }+y = x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.731 |
|
|
\[ {}\left (-2+x \right ) y^{\prime \prime }+3 y^{\prime }+\frac {4 y}{x^{2}} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.487 |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.514 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.474 |
|
|
\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.664 |
|
|
\[ {}y^{\prime \prime } = x^{n} \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.662 |
|
|
\[ {}y^{\prime \prime } = \cos \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.073 |
|
|
\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.981 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.61 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.52 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.421 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \cos \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.505 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.281 |
|
|
\[ {}y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.694 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 2 \sin \left (x \right ) {\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.536 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x^{2}+2 x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.964 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x +\sin \left (2 x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
4.503 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} {\mathrm e}^{-x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.137 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.844 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.628 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (y^{\prime }+1\right ) = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.169 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.478 |
|
|
\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.721 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.713 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 10 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.01 |
|
|
\[ {}2 y^{\prime \prime }+y^{\prime } = 2 x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.31 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.269 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x -\frac {1}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.462 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.035 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-2 x \right ) y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.774 |
|
|
\[ {}y^{\prime \prime } = 9 x^{2}+2 x -1 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.609 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime } = -3 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.546 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.651 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 5 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.078 |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y = \ln \left (1+x \right )^{2}+x -1 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.375 |
|
|
\[ {}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y = 6 x \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.28 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {2}{x^{3}} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.133 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = -\frac {2}{x}-\ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.816 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.218 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.717 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 2 x \,{\mathrm e}^{x}-1 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.059 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.867 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }-y = x +\frac {1}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.536 |
|
|
\[ {}y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1} = 0 \] |
1 |
1 |
1 |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.795 |
|
|
\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (1+x \right )^{2}} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.504 |
|
|
\[ {}y^{\prime \prime } = 2+x \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.586 |
|
|
\[ {}y^{\prime \prime } = 1+3 x \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.64 |
|
|
\[ {}y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.586 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.038 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.88 |
|
|
\[ {}\left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.356 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.278 |
|
|
\[ {}x y^{\prime \prime }-2 y^{\prime } = x^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.16 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.368 |
|
|
\[ {}x y^{\prime \prime }-3 y^{\prime } = 5 x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
6.202 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 12 x -10 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
5.402 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 10 x^{4}+2 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.957 |
|
|
\[ {}y^{\prime \prime } = \tan \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
20.485 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
9.974 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {2}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
7.598 |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.213 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.608 |
|
|
\[ {}t y^{\prime \prime }-y^{\prime } = 2 t^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.659 |
|
|
\[ {}x y^{\prime \prime } = y^{\prime }+x^{5} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.078 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+x = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.556 |
|
|
\[ {}t y^{\prime \prime }+4 y^{\prime } = t^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.355 |
|
|
\[ {}\left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.044 |
|
|
\[ {}t y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.972 |
|
|
\[ {}y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.726 |
|
|
\[ {}y^{\prime \prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.167 |
|
|
\[ {}y^{\prime \prime } = f \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.664 |
|
|
\[ {}y^{\prime \prime } = k \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.232 |
|
|
\[ {}y^{\prime \prime } = 4 \sin \left (x \right )-4 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
2.115 |
|
|
\[ {}y^{\prime \prime } = \frac {1}{x} \] |
1 |
0 |
0 |
[[_2nd_order, _quadrature]] |
✗ |
N/A |
0.247 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \frac {1}{x} \] |
1 |
0 |
0 |
[[_2nd_order, _missing_y]] |
✗ |
N/A |
0.305 |
|
|
\[ {}y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.064 |
|
|
\[ {}a y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.092 |
|
|
\[ {}y^{\prime \prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.986 |
|
|
\[ {}y^{\prime \prime } = x \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.036 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.35 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.96 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.497 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.809 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.117 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 1+x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.456 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x^{2}+x +1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.502 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x^{3}+x^{2}+x +1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.882 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.535 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \cos \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.253 |
|
|
\[ {}y^{\prime \prime }-\frac {2 y}{x^{2}} = x \,{\mathrm e}^{-\sqrt {x}} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.401 |
|
|
\[ {}y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.749 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.614 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.478 |
|
|
\[ {}x y^{\prime \prime }-x y^{\prime }-y-x \left (1+x \right ) {\mathrm e}^{x} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.437 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y-x^{2} a = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.91 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x +a \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.319 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.836 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y-x \sin \left (x \right )-\left (x^{2} a +12 a +4\right ) \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
8.401 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.895 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y-\ln \left (x \right ) x^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.193 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-2 \cos \left (x \right )+2 x = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.898 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+a x y^{\prime }+\left (a -2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.84 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.871 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-a = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.484 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 \left (v -1\right ) x y^{\prime }-2 v y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.973 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.415 |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+a y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.707 |
|
|
\[ {}x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{\frac {7}{3}} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
10.214 |
|
|
\[ {}\left (-2+x \right )^{2} y^{\prime \prime }-\left (-2+x \right ) y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.362 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-\left (2 x^{2}+l -5 x \right ) y^{\prime }-\left (4 x -1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.983 |
|
|
\[ {}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1 = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.525 |
|
|
\[ {}\left (3 x -1\right )^{2} y^{\prime \prime }+3 \left (3 x -1\right ) y^{\prime }-9 y-\ln \left (3 x -1\right )^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.682 |
|
|
\[ {}\left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.988 |
|
|
\[ {}\left (x^{2} a +b x \right ) y^{\prime \prime }+2 b y^{\prime }-2 a y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.225 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (x^{2}-1\right ) y^{\prime }-2 x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.48 |
|
|
\[ {}x \left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime }-6 x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.017 |
|
|
\[ {}y^{\prime \prime } = -\frac {2 \left (-2+x \right ) y^{\prime }}{x \left (-1+x \right )}+\frac {2 \left (1+x \right ) y}{x^{2} \left (-1+x \right )} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.983 |
|
|
\[ {}y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+a y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.445 |
|
|
\[ {}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a n \,x^{n -1}+b m \,x^{m -1}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
13.078 |
|
|
\[ {}x y^{\prime \prime }+a x y^{\prime }+a y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.615 |
|
|
\[ {}x y^{\prime \prime }+\left (x^{2} a +b x +c \right ) y^{\prime }+\left (2 x a +b \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.134 |
|
|
\[ {}x y^{\prime \prime }+x \left (x^{2} a +b \right ) y^{\prime }+\left (3 x^{2} a +b \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.438 |
|
|
\[ {}x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+a n \,x^{n -1} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
11.605 |
|
|
\[ {}\left (x +a \right ) y^{\prime \prime }+\left (b x +c \right ) y^{\prime }+b y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.398 |
|
|
\[ {}\left (x +\gamma \right ) y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a n \,x^{n -1}+b m \,x^{m -1}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
14.594 |
|
|
\[ {}\left (x^{2}+a \right ) y^{\prime \prime }+2 b x y^{\prime }+2 \left (b -1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.75 |
|
|
\[ {}\left (x^{2} a +b x +c \right ) y^{\prime \prime }+\left (d x +k \right ) y^{\prime }+\left (d -2 a \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
25.05 |
|
|
\[ {}x \left (x^{2} a +b \right ) y^{\prime \prime }+2 \left (x^{2} a +b \right ) y^{\prime }-2 a x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.434 |
|
|
\[ {}\left (a \,x^{n}+b x +c \right ) y^{\prime \prime } = a n \left (n -1\right ) x^{n -2} y \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
53.536 |
|
|
\[ {}y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a \lambda \,{\mathrm e}^{\lambda x}+b \mu \,{\mathrm e}^{\mu x}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.144 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{2 x}+1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.929 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.465 |
|
|
\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.692 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = x \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.149 |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }+4 \left (-1+x \right ) y^{\prime }+2 y = \cos \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.064 |
|
|
\[ {}\left (x^{2}-x \right ) y^{\prime \prime }+\left (4 x +2\right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.688 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.316 |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 \sin \left (x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.695 |
|
|
\[ {}x^{\prime \prime } = -3 \sqrt {t} \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.354 |
|
|
\[ {}x^{\prime }+t x^{\prime \prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.283 |
|
|
\[ {}x^{\prime \prime }+x^{\prime } = 3 t \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.671 |
|
|
\[ {}x^{\prime \prime }-2 x^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.146 |
|
|
\[ {}x^{\prime \prime }-2 x^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.262 |
|
|
\[ {}x^{\prime \prime }-x^{\prime } = 6+{\mathrm e}^{2 t} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.875 |
|
|
\[ {}x^{\prime \prime }-2 x^{\prime } = 4 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.99 |
|
|
\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }+x = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.817 |
|
|
\[ {}t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t} = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
3.08 |
|
|
\[ {}t^{2} x^{\prime \prime }-2 x = t^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.755 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.784 |
|
|
\[ {}\left (2 x +1\right ) \left (1+x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = \left (2 x +1\right )^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.093 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.827 |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
4.321 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = 4 x -8 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.48 |
|
|
\[ {}\left (2+x \right )^{2} y^{\prime \prime }-\left (2+x \right ) y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.864 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.386 |
|
|
\[ {}x^{\prime \prime }-4 x^{\prime } = t^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.224 |
|
|
\[ {}t^{2} x^{\prime \prime }-2 x = t^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.075 |
|
|
\[ {}x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
12.559 |
|
|
\[ {}t^{2} x^{\prime \prime }+t x^{\prime }-x = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
4.306 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.656 |
|
|
\[ {}3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
4.325 |
|
|
\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.149 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.134 |
|
|
\[ {}x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.228 |
|
|
\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+4 x y = 2 x \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.698 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 1-2 x \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.099 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 2 x \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.692 |
|
|
\[ {}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = \cos \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.141 |
|
|
\[ {}y^{\prime \prime }+\cot \left (x \right ) y^{\prime }-\csc \left (x \right )^{2} y = \cos \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
21.72 |
|
|
\[ {}x \ln \left (x \right ) y^{\prime \prime }+2 y^{\prime }-\frac {y}{x} = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.807 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.401 |
|
|
\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.6 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.897 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 2-6 x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.148 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.733 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.487 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.987 |
|
|
\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.641 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 3 t +2 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.078 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 3 t +2 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.102 |
|
|
\[ {}y^{\prime \prime } = \frac {1+x}{-1+x} \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.842 |
|
|
\[ {}x^{2} y^{\prime \prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.615 |
|
|
\[ {}y^{\prime \prime } = \sin \left (2 x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.073 |
|
|
\[ {}y^{\prime \prime }-3 = x \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.625 |
|
|
\[ {}x y^{\prime \prime }+2 = \sqrt {x} \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.524 |
|
|
\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.438 |
|
|
\[ {}x y^{\prime \prime } = 2 y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.237 |
|
|
\[ {}y^{\prime \prime } = y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.737 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.638 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.174 |
|
|
\[ {}y^{\prime \prime } = 2 y^{\prime }-6 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.451 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.694 |
|
|
\[ {}y^{\prime \prime } = y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.634 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = 6 x^{5} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.281 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.542 |
|
|
\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.672 |
|
|
\[ {}x y^{\prime \prime } = 2 y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.525 |
|
|
\[ {}y^{\prime \prime } = y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.114 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.023 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime } = 6 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.515 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.049 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.973 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.531 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.679 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{\frac {x}{2}} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.729 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.344 |
|
|
\[ {}y^{\prime \prime } = 6 x \,{\mathrm e}^{x} \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
2.779 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 20 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.543 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.74 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 85 \cos \left (2 \ln \left (x \right )\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
14.775 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = 15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.625 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = \frac {10}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.096 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = \sqrt {x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.602 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = \frac {1}{-2+x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.904 |
|
|
\[ {}x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.189 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = \frac {10}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.388 |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime } = \sqrt {x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.704 |
|
|
\[ {}2 y^{\prime \prime }-7 y^{\prime }+3 = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.789 |
|
|
\[ {}x y^{\prime \prime } = 3 y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.601 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.03 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = \frac {1}{x^{2}+1} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.786 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1+x \right )^{2}} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.776 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.302 |
|
|
\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.816 |
|
|
\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.472 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.97 |
|
|
\[ {}y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.84 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.27 |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.337 |
|
|
\[ {}3 y^{\prime \prime }-y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.742 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 3-4 t \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.054 |
|
|
\[ {}y^{\prime \prime } = 3 t^{4}-2 t \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.902 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 52 \sin \left (3 t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.997 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.337 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.58 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.517 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.22 |
|
|
\[ {}y^{\prime \prime } = t^{2}+{\mathrm e}^{t}+\sin \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
3.571 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 18 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.643 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = -{\mathrm e}^{3 t}-2 t \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.026 |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = -3 t -4 t^{2} {\mathrm e}^{2 t} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.357 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 2 t^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.508 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.844 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = {\mathrm e}^{-3 t}-{\mathrm e}^{3 t} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.079 |
|
|
\[ {}y^{\prime \prime }+16 y^{\prime } = t \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.14 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = \ln \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
5.294 |
|
|
\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 2 \ln \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.653 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x^{2}} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.778 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
8.766 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
4.191 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
4.118 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 5 t^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.464 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = -3 \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.441 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = \frac {1}{{\mathrm e}^{2 t}+1} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.274 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
6.456 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.053 |
|
|
\[ {}y^{\prime \prime } \left (2+x \right )^{5} = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.948 |
|
|
\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.001 |
|
|
\[ {}y^{\prime \prime } = 2 x \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.646 |
|
|
\[ {}x y^{\prime \prime } = y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.02 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.675 |
|
|
\[ {}x y^{\prime \prime } = y^{\prime }+x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.184 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+2 = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.143 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 3 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.917 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime } = \left (-1+x \right )^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.098 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.07 |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime } = {\mathrm e}^{-7 x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.112 |
|
|
\[ {}4 y^{\prime \prime }-3 y^{\prime } = x \,{\mathrm e}^{\frac {3 x}{4}} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.201 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = x \,{\mathrm e}^{4 x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.064 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = -2 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.509 |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime } = 8 x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.697 |
|
|
\[ {}7 y^{\prime \prime }-y^{\prime } = 14 x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.685 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 3 x \,{\mathrm e}^{-3 x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.924 |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.687 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 4 \left (\cos \left (x \right )+\sin \left (x \right )\right ) {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
4.516 |
|
|
\[ {}4 y^{\prime \prime }+8 y^{\prime } = x \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
5.262 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = x +{\mathrm e}^{-4 x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.099 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 2 \cos \left (4 x \right )^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
5.691 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 18 x -10 \cos \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
4.339 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
10.406 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.491 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.404 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+1 = 3 \sin \left (2 x \right )+\cos \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.422 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.381 |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = -5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.992 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.964 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.899 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.774 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = \sin \left (\ln \left (x \right )\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.589 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = -\frac {16 \ln \left (x \right )}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.35 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.67 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 \ln \left (x \right )^{2}+12 x \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.657 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \frac {1}{1+{\mathrm e}^{x}} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.326 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.529 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {1}{x^{2}+1} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.061 |
|
|
\[ {}y^{\prime \prime }+\alpha y^{\prime } = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.14 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.819 |
|
|
|
||||||||
|
|
||||||||
|
|