|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = -F \left (x \right ) \left (x^{2}+2 x y-y^{2}\right )+\frac {y}{x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
2.654 |
|
|
\[
{}y^{\prime } = -F \left (x \right ) \left (-7 x y^{2}-x^{3}\right )+\frac {y}{x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
2.216 |
|
|
\[
{}y^{\prime } = -F \left (x \right ) \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{\ln \left (x \right ) x}
\] |
[_Riccati] |
✓ |
2.836 |
|
|
\[
{}y^{\prime } = -x^{3} \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{\ln \left (x \right ) x}
\] |
[_Riccati] |
✓ |
3.403 |
|
|
\[
{}y^{\prime } = \left (y-{\mathrm e}^{x}\right )^{2}+{\mathrm e}^{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
1.658 |
|
|
\[
{}y^{\prime } = \frac {\left (y-\operatorname {Si}\left (x \right )\right )^{2}+\sin \left (x \right )}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
6.385 |
|
|
\[
{}y^{\prime } = \left (y+\cos \left (x \right )\right )^{2}+\sin \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.354 |
|
|
\[
{}y^{\prime } = \frac {\left (y-\ln \left (x \right )-\operatorname {Ci}\left (x \right )\right )^{2}+\cos \left (x \right )}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
52.435 |
|
|
\[
{}y^{\prime } = \frac {\left (y-x +\ln \left (x +1\right )\right )^{2}+x}{x +1}
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
2.269 |
|
|
\[
{}y^{\prime } = \frac {2 x^{2} y+x^{3}+y \ln \left (x \right ) x -y^{2}-x y}{x^{2} \left (x +\ln \left (x \right )\right )}
\] |
[_Riccati] |
✓ |
2.670 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.078 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.210 |
|
|
\[
{}y^{\prime \prime }+y-\sin \left (n x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.490 |
|
|
\[
{}y^{\prime \prime }+y-a \cos \left (b x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.607 |
|
|
\[
{}y^{\prime \prime }+y-\sin \left (a x \right ) \sin \left (b x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
12.971 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.253 |
|
|
\[
{}y^{\prime \prime }-2 y-4 x^{2} {\mathrm e}^{x^{2}} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.544 |
|
|
\[
{}y^{\prime \prime }+a^{2} y-\cot \left (a x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.798 |
|
|
\[
{}y^{\prime \prime }+l y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.139 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.671 |
|
|
\[
{}y^{\prime \prime }-\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.855 |
|
|
\[
{}y^{\prime \prime }-\left (x^{2}+a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.393 |
|
|
\[
{}y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.922 |
|
|
\[
{}y^{\prime \prime }-c \,x^{a} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.856 |
|
|
\[
{}y^{\prime \prime }-\left (a^{2} x^{2 n}-1\right ) y = 0
\] |
[_Titchmarsh] |
✗ |
0.262 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{2 c}+b \,x^{c -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.274 |
|
|
\[
{}y^{\prime \prime }+\left ({\mathrm e}^{2 x}-v^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.707 |
|
|
\[
{}y^{\prime \prime }+a \,{\mathrm e}^{b x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.733 |
|
|
\[
{}y^{\prime \prime }-\left (4 a^{2} b^{2} x^{2} {\mathrm e}^{2 b \,x^{2}}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.305 |
|
|
\[
{}y^{\prime \prime }+\left (a \,{\mathrm e}^{2 x}+b \,{\mathrm e}^{x}+c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.313 |
|
|
\[
{}y^{\prime \prime }+\left (a \cosh \left (x \right )^{2}+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.732 |
|
|
\[
{}y^{\prime \prime }+\left (a \cos \left (2 x \right )+b \right ) y = 0
\] |
[_ellipsoidal] |
✗ |
0.638 |
|
|
\[
{}y^{\prime \prime }+\left (a \cos \left (x \right )^{2}+b \right ) y = 0
\] |
[_ellipsoidal] |
✗ |
0.856 |
|
|
\[
{}y^{\prime \prime }-\left (1+2 \tan \left (x \right )^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.819 |
|
|
\[
{}y^{\prime \prime }-\left (\frac {m \left (m -1\right )}{\cos \left (x \right )^{2}}+\frac {n \left (n -1\right )}{\sin \left (x \right )^{2}}+a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
5.550 |
|
|
\[
{}y^{\prime \prime }-\left (n \left (n +1\right ) \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )+B \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.256 |
|
|
\[
{}y^{\prime \prime }-\left (n \left (n +1\right ) k^{2} \operatorname {JacobiSN}\left (x , k\right )^{2}+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.299 |
|
|
\[
{}y^{\prime \prime }-\left (\frac {p^{\prime \prime \prime \prime }\left (x \right )}{30}+\frac {7 p^{\prime \prime }\left (x \right )}{3}+a p \left (x \right )+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.711 |
|
|
\[
{}y^{\prime \prime }-\left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.307 |
|
|
\[
{}y^{\prime \prime }+\left (P \left (x \right )+l \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.266 |
|
|
\[
{}y^{\prime \prime }-f \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.231 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+a \,{\mathrm e}^{-2 x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.539 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.036 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.090 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b y-f \left (x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.605 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }-\left (b^{2} x^{2}+c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.586 |
|
|
\[
{}y^{\prime \prime }+2 a y^{\prime }+f \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.334 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.144 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.454 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (n +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.516 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x -n y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.528 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[_Hermite] |
✓ |
1.257 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -a y = 0
\] |
[_Hermite] |
✗ |
0.537 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.290 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +a y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.527 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.698 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (3 x^{2}+2 n -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.565 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-1\right ) y-{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.812 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.760 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-3\right ) y-{\mathrm e}^{x^{2}} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.170 |
|
|
\[
{}y^{\prime \prime }+a x y^{\prime }+b y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.605 |
|
|
\[
{}y^{\prime \prime }+2 a x y^{\prime }+a^{2} x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
33.371 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.787 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.474 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.544 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-\left (x +1\right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.336 |
|
|
\[
{}y^{\prime \prime }-x^{2} \left (x +1\right ) y^{\prime }+x \left (x^{4}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.257 |
|
|
\[
{}y^{\prime \prime }+x^{4} y^{\prime }-x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.750 |
|
|
\[
{}y^{\prime \prime }+a \,x^{q -1} y^{\prime }+b \,x^{q -2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.600 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } \sqrt {x}+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{{3}/{2}}}{3}} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.632 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.278 |
|
|
\[
{}y^{\prime \prime }-\left (2 \,{\mathrm e}^{x}+1\right ) y^{\prime }+{\mathrm e}^{2 x} y-{\mathrm e}^{3 x} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.656 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+\tan \left (x \right )+b y = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
26.655 |
|
|
\[
{}y^{\prime \prime }+2 n y^{\prime } \cot \left (x \right )+\left (-a^{2}+n^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.686 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } \tan \left (x \right )+y \cos \left (x \right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.439 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } \tan \left (x \right )-y \cos \left (x \right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.893 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } \cot \left (x \right )+v \left (v +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.286 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } \cot \left (x \right )+y \sin \left (x \right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.538 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime } \tan \left (x \right )+b y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.452 |
|
|
\[
{}y^{\prime \prime }+2 a y^{\prime } \cot \left (a x \right )+\left (-a^{2}+b^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.846 |
|
|
\[
{}y^{\prime \prime }+a p^{\prime \prime }\left (x \right ) y^{\prime }+\left (a +b p \left (x \right )-4 n a p \left (x \right )^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.835 |
|
|
\[
{}y^{\prime \prime }+\frac {\left (11 \operatorname {WeierstrassP}\left (x , a , b\right ) \operatorname {WeierstrassPPrime}\left (x , a , b\right )-6 \operatorname {WeierstrassP}\left (x , a , b\right )^{2}+\frac {a}{2}\right ) y^{\prime }}{\operatorname {WeierstrassPPrime}\left (x , a , b\right )+\operatorname {WeierstrassP}\left (x , a , b\right )^{2}}+\frac {\left (\operatorname {WeierstrassPPrime}\left (x , a , b\right )^{2}-\operatorname {WeierstrassP}\left (x , a , b\right )^{2} \operatorname {WeierstrassPPrime}\left (x , a , b\right )-\operatorname {WeierstrassP}\left (x , a , b\right ) \left (6 \operatorname {WeierstrassP}\left (x , a , b\right )^{2}-\frac {a}{2}\right )\right ) y}{\operatorname {WeierstrassPPrime}\left (x , a , b\right )+\operatorname {WeierstrassP}\left (x , a , b\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
42.473 |
|
|
\[
{}y^{\prime \prime }+f \left (x \right ) y^{\prime }+g \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.488 |
|
|
\[
{}y^{\prime \prime }+f \left (x \right ) y^{\prime }+\left (f^{\prime }\left (x \right )+a \right ) y-g \left (x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.417 |
|
|
\[
{}y^{\prime \prime }+\left (a f \left (x \right )+b \right ) y^{\prime }+\left (c f \left (x \right )+d \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.503 |
|
|
\[
{}y^{\prime \prime }+f \left (x \right ) y^{\prime }+\left (\frac {f \left (x \right )^{2}}{4}+\frac {f^{\prime }\left (x \right )}{2}+a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.151 |
|
|
\[
{}y^{\prime \prime }-\frac {a f^{\prime }\left (x \right ) y^{\prime }}{f \left (x \right )}+b f \left (x \right )^{2 a} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.525 |
|
|
\[
{}y^{\prime \prime }-\left (\frac {f^{\prime }\left (x \right )}{f \left (x \right )}+2 a \right ) y^{\prime }+\left (\frac {a f^{\prime }\left (x \right )}{f \left (x \right )}+a^{2}-b^{2} f \left (x \right )^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.014 |
|
|
\[
{}y^{\prime \prime }+\frac {f \left (x \right ) f^{\prime \prime \prime }\left (x \right ) y^{\prime }}{f \left (x \right )^{2}+b^{2}}-\frac {a^{2} {f^{\prime }\left (x \right )}^{2} y}{f \left (x \right )^{2}+b^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.241 |
|
|
\[
{}y^{\prime \prime }-\left (\frac {2 f^{\prime }\left (x \right )}{f \left (x \right )}+\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}-\frac {g^{\prime }\left (x \right )}{g \left (x \right )}\right ) y^{\prime }+\left (\frac {f^{\prime }\left (x \right ) \left (\frac {2 f^{\prime }\left (x \right )}{f \left (x \right )}+\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}-\frac {g^{\prime }\left (x \right )}{g \left (x \right )}\right )}{f \left (x \right )}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}-\frac {v^{2} {g^{\prime }\left (x \right )}^{2}}{g \left (x \right )^{2}}+{g^{\prime }\left (x \right )}^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.844 |
|
|
\[
{}y^{\prime \prime }-\left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 v -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}+\frac {2 h^{\prime }\left (x \right )}{h \left (x \right )}\right ) y^{\prime }+\left (\frac {h^{\prime }\left (x \right ) \left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 v -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}+\frac {2 h^{\prime }\left (x \right )}{h \left (x \right )}\right )}{h \left (x \right )}-\frac {h^{\prime \prime }\left (x \right )}{h \left (x \right )}+{g^{\prime }\left (x \right )}^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.855 |
|
|
\[
{}4 y^{\prime \prime }+9 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.005 |
|
|
\[
{}4 y^{\prime \prime }-\left (x^{2}+a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.388 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime } \tan \left (x \right )-\left (5 \tan \left (x \right )^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.941 |
|
|
\[
{}a y^{\prime \prime }-\left (a b +c +x \right ) y^{\prime }+\left (b \left (x +c \right )+d \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.918 |
|
|
\[
{}a^{2} y^{\prime \prime }+a \left (a^{2}-2 b \,{\mathrm e}^{-a x}\right ) y^{\prime }+b^{2} {\mathrm e}^{-2 a x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.569 |
|
|
\[
{}x \left (y^{\prime \prime }+y\right )-\cos \left (x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.938 |
|
|
\[
{}x y^{\prime \prime }+\left (x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.486 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.864 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+a y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.770 |
|