second order ode’s with missing dependent variable \(y(x)\). Reference this
Number of problems in this table is 356
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 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.728 |
|
|
\[ {}2 y^{\prime \prime }-3 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.945 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \] |
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 |
|
|
\[ {}y^{\prime \prime } = 0 \] |
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 |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = {\mathrm e}^{2 x} \sin \left (x \right ) x \] |
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 |
|
|
\[ {}y^{\prime \prime } = \cos \left (t \right ) \] |
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 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (1+y^{\prime }\right ) = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.365 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime } \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
7.569 |
|
|
\[ {}x y^{\prime \prime }+x = y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
4.142 |
|
|
\[ {}x^{\prime \prime }+t x^{\prime } = t^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.288 |
|
|
\[ {}x^{2} y^{\prime \prime } = x y^{\prime }+1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.694 |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.811 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
5.097 |
|
|
\[ {}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \] |
2 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
8.321 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{2}+y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
3.574 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
2.329 |
|
|
\[ {}y^{\prime \prime }+2 {y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.163 |
|
|
\[ {}y^{\prime \prime }+2 {y^{\prime }}^{2} = 2 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
5.403 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = {y^{\prime }}^{3} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
5.674 |
|
|
\[ {}y^{\prime \prime } = \sec \left (x \right ) \tan \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
3.814 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{2} \cos \left (x \right ) \] |
1 |
1 |
0 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
2.165 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
6.265 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{2} \sin \left (x \right ) \] |
1 |
1 |
0 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.766 |
|
|
\[ {}\left (-{\mathrm e}^{x}+1\right ) y^{\prime \prime } = {\mathrm e}^{x} y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.575 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.794 |
|
|
\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \] |
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 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x} = 9 x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.858 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.61 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 0 \] |
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 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.115 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.628 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.483 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (1+y^{\prime }\right ) = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.169 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.986 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.478 |
|
|
\[ {}\left (1+{y^{\prime }}^{2}\right )^{3} = a^{2} {y^{\prime \prime }}^{2} \] |
2 |
4 |
4 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
4.842 |
|
|
\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \] |
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 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.459 |
|
|
\[ {}x y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime } \] |
1 |
1 |
2 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.659 |
|
|
\[ {}{y^{\prime \prime }}^{2} = k^{2} \left (1+{y^{\prime }}^{2}\right ) \] |
2 |
4 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.845 |
|
|
\[ {}k = \frac {y^{\prime \prime }}{\left (1+y^{\prime }\right )^{\frac {3}{2}}} \] |
2 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear]] |
✓ |
✓ |
1.687 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.035 |
|
|
\[ {}y^{\prime \prime } = 9 x^{2}+2 x -1 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.609 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime } = -3 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.546 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime } = x^{3} {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.254 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.531 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 5 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.078 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.191 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {2}{x^{3}} \] |
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 |
|
|
\[ {}u^{\prime \prime }-\cot \left (\theta \right ) u^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.991 |
|
|
\[ {}y^{\prime \prime } = 2+x \] |
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 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.278 |
|
|
\[ {}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } = {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.932 |
|
|
\[ {}x y^{\prime \prime }-2 y^{\prime } = x^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.16 |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.777 |
|
|
\[ {}y^{\prime \prime } = -\frac {1}{2 {y^{\prime }}^{2}} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
8.194 |
|
|
\[ {}\frac {y^{\prime \prime }}{y^{\prime }} = x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.948 |
|
|
\[ {}y^{\prime \prime } y^{\prime } = \left (1+x \right ) x \] |
1 |
2 |
2 |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
3.369 |
|
|
\[ {}x^{2} y^{\prime \prime } = 2 x y^{\prime }+{y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.188 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.368 |
|
|
\[ {}\left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
65.544 |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
3.93 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = 1 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
9.789 |
|
|
\[ {}x y^{\prime \prime } = y^{\prime }-2 {y^{\prime }}^{3} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
15.584 |
|
|
\[ {}x y^{\prime \prime }-3 y^{\prime } = 5 x \] |
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 |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = 0 \] |
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 |
|
|
\[ {}y^{\prime \prime } = x {y^{\prime }}^{3} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.338 |
|
|
\[ {}x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.013 |
|
|
\[ {}x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.807 |
|
|
\[ {}2 a y^{\prime \prime }+{y^{\prime }}^{3} = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.347 |
|
|
\[ {}x y^{\prime \prime } = y^{\prime }+x^{5} \] |
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 |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime } = y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.085 |
|
|
\[ {}y^{\prime \prime } = x {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.128 |
|
|
\[ {}y^{\prime \prime } = x {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.937 |
|
|
\[ {}x^{3} y^{\prime \prime }-x^{2} y^{\prime } = -x^{2}+3 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.612 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.592 |
|
|
\[ {}y^{\prime \prime } = {\mathrm e}^{x} {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.592 |
|
|
\[ {}2 y^{\prime \prime } = {y^{\prime }}^{3} \sin \left (2 x \right ) \] |
1 |
2 |
2 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
3.171 |
|
|
\[ {}x^{2} y^{\prime \prime }+{y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.645 |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.585 |
|
|
\[ {}y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \] |
2 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
5.48 |
|
|
\[ {}x^{2} y^{\prime \prime } = y^{\prime } \left (2 x -y^{\prime }\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.155 |
|
|
\[ {}x^{2} y^{\prime \prime } = y^{\prime } \left (3 x -2 y^{\prime }\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.875 |
|
|
\[ {}x y^{\prime \prime } = y^{\prime } \left (2-3 x y^{\prime }\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.083 |
|
|
\[ {}x^{4} y^{\prime \prime } = y^{\prime } \left (y^{\prime }+x^{3}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.091 |
|
|
\[ {}y^{\prime \prime } = 2 x +\left (x^{2}-y^{\prime }\right )^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.299 |
|
|
\[ {}{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2} = 0 \] |
2 |
4 |
2 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
141.525 |
|
|
\[ {}{y^{\prime \prime }}^{2}-x y^{\prime \prime }+y^{\prime } = 0 \] |
2 |
2 |
2 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.686 |
|
|
\[ {}{y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right ) \] |
3 |
1 |
3 |
[[_2nd_order, _missing_y]] |
✓ |
✗ |
126.669 |
|
|
\[ {}t y^{\prime \prime }+4 y^{\prime } = t^{2} \] |
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 |
|
|
\[ {}t^{2} y^{\prime \prime }-2 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.863 |
|
|
\[ {}y^{\prime \prime } = 0 \] |
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 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.336 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✗ |
94.947 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+1+x {y^{\prime }}^{2} = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.063 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
2.509 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{3} = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
2.088 |
|
|
\[ {}y^{\prime \prime } = \frac {1}{x} \] |
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 |
|
|
\[ {}{y^{\prime \prime }}^{2} = 0 \] |
2 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.779 |
|
|
\[ {}{y^{\prime \prime }}^{n} = 0 \] |
0 |
2 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.619 |
|
|
\[ {}a y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.092 |
|
|
\[ {}a {y^{\prime \prime }}^{2} = 0 \] |
2 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.717 |
|
|
\[ {}a {y^{\prime \prime }}^{n} = 0 \] |
0 |
2 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.572 |
|
|
\[ {}y^{\prime \prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.986 |
|
|
\[ {}{y^{\prime \prime }}^{2} = 1 \] |
2 |
2 |
2 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.793 |
|
|
\[ {}y^{\prime \prime } = x \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.036 |
|
|
\[ {}{y^{\prime \prime }}^{2} = x \] |
2 |
2 |
2 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.783 |
|
|
\[ {}{y^{\prime \prime }}^{3} = 0 \] |
3 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.933 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.35 |
|
|
\[ {}{y^{\prime \prime }}^{2}+y^{\prime } = 0 \] |
2 |
6 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
7.969 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.861 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.96 |
|
|
\[ {}{y^{\prime \prime }}^{2}+y^{\prime } = 1 \] |
2 |
6 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
10.206 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = 1 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
3.548 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.497 |
|
|
\[ {}{y^{\prime \prime }}^{2}+y^{\prime } = x \] |
2 |
2 |
2 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.847 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.054 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 1 \] |
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 |
|
|
\[ {}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+{y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
3.006 |
|
|
\[ {}y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.749 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.478 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.836 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+2 = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
4.165 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
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 |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+\left (\left (1+a \right ) x +b \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.303 |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+\left (\left (\operatorname {a1} +\operatorname {b1} +1\right ) x -\operatorname {d1} \right ) y^{\prime }+\operatorname {a1} \operatorname {b1} \operatorname {d1} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
17.26 |
|
|
\[ {}\left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.988 |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+2 x \left (3 x +2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.526 |
|
|
\[ {}y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}} \] |
2 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
4.01 |
|
|
\[ {}y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}+b \] |
2 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
194.412 |
|
|
\[ {}y^{\prime \prime } = a \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \] |
2 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
4.207 |
|
|
\[ {}y^{\prime \prime }-2 a x \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} = 0 \] |
2 |
1 |
3 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
2.19 |
|
|
\[ {}8 y^{\prime \prime }+9 {y^{\prime }}^{4} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.146 |
|
|
\[ {}2 x y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
2.002 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.842 |
|
|
\[ {}\left (a \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }\right ) y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0 \] |
2 |
2 |
4 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
5.132 |
|
|
\[ {}a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime } = 0 \] |
2 |
3 |
2 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.154 |
|
|
\[ {}y^{\prime \prime }+a \,x^{n} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.786 |
|
|
\[ {}x y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+c x \left (-c \,x^{2}+x a +b +1\right ) = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
72.239 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{2 x}+1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.929 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.408 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime } = x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.628 |
|
|
\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.692 |
|
|
\[ {}\left (y^{\prime }-x y^{\prime \prime }\right )^{2} = 1+{y^{\prime \prime }}^{2} \] |
2 |
4 |
3 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.21 |
|
|
\[ {}y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }+2 \tan \left (x \right ) {y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.154 |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.786 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 2 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
4.341 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.316 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.327 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
4.49 |
|
|
\[ {}x^{\prime \prime } = -3 \sqrt {t} \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.354 |
|
|
\[ {}x^{\prime }+t x^{\prime \prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.283 |
|
|
\[ {}\frac {x^{\prime }+t x^{\prime \prime }}{t} = -2 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.619 |
|
|
\[ {}x^{\prime \prime }+x^{\prime } = 3 t \] |
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 |
|
|
\[ {}t^{2} x^{\prime \prime }+t x^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.187 |
|
|
\[ {}x^{\prime \prime }+t^{2} x^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
4.904 |
|
|
\[ {}x^{\prime \prime }+\frac {x^{\prime }}{t} = a \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.708 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 0 \] |
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 |
|
|
\[ {}x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
12.559 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.81 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.799 |
|
|
\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.149 |
|
|
\[ {}m x^{\prime \prime } = f \left (x^{\prime }\right ) \] |
0 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.896 |
|
|
\[ {}{y^{\prime \prime }}^{3}+y^{\prime \prime }+1 = x \] |
3 |
3 |
3 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
3.099 |
|
|
\[ {}x y^{\prime \prime } = y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right ) \] |
0 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.787 |
|
|
\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.6 |
|
|
\[ {}y^{\prime \prime } = \frac {1}{2 y^{\prime }} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
1.533 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.897 |
|
|
\[ {}y^{\prime \prime }+\tan \left (x \right ) y^{\prime } = \sin \left (2 x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.233 |
|
|
\[ {}{y^{\prime \prime }}^{2}+{y^{\prime }}^{2} = a^{2} \] |
2 |
2 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
4.263 |
|
|
\[ {}y^{\prime \prime } = \frac {1}{2 y^{\prime }} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
1.049 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 2-6 x \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.148 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.579 |
|
|
\[ {}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.86 |
|
|
\[ {}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.83 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 3 t +2 \] |
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 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.748 |
|
|
\[ {}y^{\prime \prime } = \sin \left (2 x \right ) \] |
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 |
|
|
\[ {}x y^{\prime \prime } = y^{\prime }-2 x^{2} y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.319 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.174 |
|
|
\[ {}y^{\prime \prime } = 4 x \sqrt {y^{\prime }} \] |
2 |
1 |
3 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.045 |
|
|
\[ {}y^{\prime \prime } y^{\prime } = 1 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
2.463 |
|
|
\[ {}x y^{\prime \prime } = {y^{\prime }}^{2}-y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.948 |
|
|
\[ {}x y^{\prime \prime }-{y^{\prime }}^{2} = 6 x^{5} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.695 |
|
|
\[ {}y^{\prime \prime } = 2 y^{\prime }-6 \] |
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 |
|
|
\[ {}y^{\prime \prime } = 4 x \sqrt {y^{\prime }} \] |
2 |
1 |
3 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.939 |
|
|
\[ {}y^{\prime \prime } y^{\prime } = 1 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
1.559 |
|
|
\[ {}x y^{\prime \prime } = {y^{\prime }}^{2}-y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.815 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = 6 x^{5} \] |
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 |
|
|
\[ {}y^{\prime \prime } = y^{\prime } \left (y^{\prime }-2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.553 |
|
|
\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \] |
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 |
|
|
\[ {}2 x y^{\prime } y^{\prime \prime } = {y^{\prime }}^{2}-1 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
3.708 |
|
|
\[ {}y^{\prime \prime } = -2 x {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.859 |
|
|
\[ {}y^{\prime \prime } = -2 x {y^{\prime }}^{2} \] |
1 |
0 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
N/A |
0.65 |
|
|
\[ {}y^{\prime \prime } = -2 x {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.674 |
|
|
\[ {}y^{\prime \prime } = -2 x {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.886 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \] |
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 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.826 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.83 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{\frac {x}{2}} \] |
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 |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime } = \sqrt {x} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.704 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.581 |
|
|
\[ {}2 y^{\prime \prime }-7 y^{\prime }+3 = 0 \] |
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 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = -3 x {y^{\prime }}^{3} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.964 |
|
|
\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \] |
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 |
|
|
\[ {}y^{\prime \prime } = 0 \] |
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 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 5 t^{2} \] |
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 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.329 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.053 |
|
|
\[ {}y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \] |
2 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.97 |
|
|
\[ {}y^{\prime \prime } \left (2+x \right )^{5} = 1 \] |
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 |
|
|
\[ {}x y^{\prime \prime } = \left (2 x^{2}+1\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.651 |
|
|
\[ {}x y^{\prime \prime } = y^{\prime }+x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.184 |
|
|
\[ {}x \ln \left (x \right ) y^{\prime \prime } = y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.678 |
|
|
\[ {}2 y^{\prime \prime } = \frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
0.941 |
|
|
\[ {}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \] |
2 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.484 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.346 |
|
|
\[ {}y^{\prime \prime } = \sqrt {1-{y^{\prime }}^{2}} \] |
2 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.649 |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.721 |
|
|
\[ {}y^{\prime \prime } = \sqrt {1+y^{\prime }} \] |
2 |
3 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
5.595 |
|
|
\[ {}y^{\prime \prime } = y^{\prime } \ln \left (y^{\prime }\right ) \] |
0 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.464 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+2 = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.143 |
|
|
\[ {}y^{\prime \prime } = y^{\prime } \left (1+y^{\prime }\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.342 |
|
|
\[ {}3 y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \] |
2 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.937 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 3 \] |
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 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.774 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \frac {1}{1+{\mathrm e}^{x}} \] |
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 |
|
|
\[ {}x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime } = 4 x^{3} {\mathrm e}^{x^{2}} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.488 |
|
|
\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.468 |
|
|
\[ {}x \ln \left (x \right ) y^{\prime \prime }-y^{\prime } = \ln \left (x \right )^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.908 |
|
|
\[ {}x y^{\prime \prime }+\left (2 x -1\right ) y^{\prime } = -4 x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.764 |
|
|
\[ {}y^{\prime \prime }+\tan \left (x \right ) y^{\prime } = \cos \left (x \right ) \cot \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.911 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {1}{x^{2}+1} \] |
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 |
|
|
|
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|
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