|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime } = \frac {2 y}{\sin \left (x \right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.852 |
|
|
\[
{}y^{\prime \prime } = -\frac {a y}{\sin \left (x \right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.862 |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime \prime }-\left (a \sin \left (x \right )^{2}+n \left (n -1\right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.565 |
|
|
\[
{}y^{\prime \prime } = -\frac {\left (-a^{2} \cos \left (x \right )^{2}-\left (3-2 a \right ) \cos \left (x \right )-3+3 a \right ) y}{\sin \left (x \right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
5.176 |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime \prime }-\left (a^{2} \cos \left (x \right )^{2}+b \cos \left (x \right )+\frac {b^{2}}{\left (2 a -3\right )^{2}}+3 a +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
12.829 |
|
|
\[
{}y^{\prime \prime } = -\frac {\left (-\left (a^{2} b^{2}-\left (a +1\right )^{2}\right ) \sin \left (x \right )^{2}-a \left (a +1\right ) b \sin \left (2 x \right )-a \left (a -1\right )\right ) y}{\sin \left (x \right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
6.079 |
|
|
\[
{}y^{\prime \prime } = -\frac {\left (a \cos \left (x \right )^{2}+b \sin \left (x \right )^{2}+c \right ) y}{\sin \left (x \right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.748 |
|
|
\[
{}y^{\prime \prime } = -\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}+\frac {y}{\sin \left (x \right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.287 |
|
|
\[
{}y^{\prime \prime } = -\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (v \left (v +1\right ) \sin \left (x \right )^{2}-n^{2}\right ) y}{\sin \left (x \right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
3.744 |
|
|
\[
{}y^{\prime \prime } = \frac {\cos \left (2 x \right ) y^{\prime }}{\sin \left (2 x \right )}-2 y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.266 |
|
|
\[
{}y^{\prime \prime } = -\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (-17 \sin \left (x \right )^{2}-1\right ) y}{4 \sin \left (x \right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.310 |
|
|
\[
{}y^{\prime \prime } = -\frac {\sin \left (x \right ) y^{\prime }}{\cos \left (x \right )}-\frac {\left (2 x^{2}+x^{2} \sin \left (x \right )^{2}-24 \cos \left (x \right )^{2}\right ) y}{4 x^{2} \cos \left (x \right )^{2}}+\sqrt {\cos \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
6.829 |
|
|
\[
{}y^{\prime \prime } = -\frac {b \cos \left (x \right ) y^{\prime }}{\sin \left (x \right ) a}-\frac {\left (c \cos \left (x \right )^{2}+d \cos \left (x \right )+e \right ) y}{a \sin \left (x \right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
4.836 |
|
|
\[
{}y^{\prime \prime } = -\frac {4 \sin \left (3 x \right ) y}{\sin \left (x \right )^{3}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.622 |
|
|
\[
{}y^{\prime \prime } = -\frac {\left (4 v \left (v +1\right ) \sin \left (x \right )^{2}-\cos \left (x \right )^{2}+2-4 n^{2}\right ) y}{4 \sin \left (x \right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
3.749 |
|
|
\[
{}y^{\prime \prime } = \frac {\left (3 \sin \left (x \right )^{2}+1\right ) y^{\prime }}{\cos \left (x \right ) \sin \left (x \right )}+\frac {\sin \left (x \right )^{2} y}{\cos \left (x \right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.431 |
|
|
\[
{}y^{\prime \prime } = -\frac {\left (-a \cos \left (x \right )^{2} \sin \left (x \right )^{2}-m \left (m -1\right ) \sin \left (x \right )^{2}-n \left (n -1\right ) \cos \left (x \right )^{2}\right ) y}{\cos \left (x \right )^{2} \sin \left (x \right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
6.017 |
|
|
\[
{}y^{\prime \prime } = -\frac {x y^{\prime }}{f \left (x \right )}+\frac {y}{f \left (x \right )}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.833 |
|
|
\[
{}y^{\prime \prime } = -\frac {f^{\prime }\left (x \right ) y^{\prime }}{2 f \left (x \right )}-\frac {g \left (x \right ) y}{f \left (x \right )}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.835 |
|
|
\[
{}y^{\prime \prime } = -\frac {\left (2 f \left (x \right ) {g^{\prime }\left (x \right )}^{2} g \left (x \right )-\left (g \left (x \right )^{2}-1\right ) \left (f \left (x \right ) g^{\prime \prime }\left (x \right )+2 f^{\prime }\left (x \right ) g^{\prime }\left (x \right )\right )\right ) y^{\prime }}{f \left (x \right ) g^{\prime }\left (x \right ) \left (g \left (x \right )^{2}-1\right )}-\frac {\left (\left (g \left (x \right )^{2}-1\right ) \left (f^{\prime }\left (x \right ) \left (f \left (x \right ) g^{\prime \prime }\left (x \right )+2 f^{\prime }\left (x \right ) g^{\prime }\left (x \right )\right )-f \left (x \right ) f^{\prime \prime }\left (x \right ) g^{\prime }\left (x \right )\right )-\left (2 f^{\prime }\left (x \right ) g \left (x \right )+v \left (v +1\right ) f \left (x \right ) g^{\prime }\left (x \right )\right ) f \left (x \right ) {g^{\prime }\left (x \right )}^{2}\right ) y}{f \left (x \right )^{2} g^{\prime }\left (x \right ) \left (g \left (x \right )^{2}-1\right )}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.513 |
|
|
\[
{}y^{\prime \prime } = -\frac {y^{\prime }}{x}-\frac {\left (-1+x \right ) y}{x^{4}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.913 |
|
|
\[
{}y^{\prime \prime } = -\frac {y^{\prime }}{x}-\frac {\left (-x -1\right ) y}{x^{4}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.916 |
|
|
\[
{}y^{\prime \prime } = -\frac {b^{2} y}{\left (-a^{2}+x^{2}\right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.624 |
|
|
\[
{}y^{\prime \prime \prime }-\lambda y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime \prime }+y a \,x^{3}-b x = 0
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.037 |
|
|
\[
{}y^{\prime \prime \prime }-a \,x^{b} y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.038 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime }-4 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.061 |
|
|
\[
{}y^{\prime \prime \prime }-a^{2} y^{\prime }-{\mathrm e}^{2 a x} \sin \left (x \right )^{2} = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.298 |
|
|
\[
{}y^{\prime \prime \prime }+2 a x y^{\prime }+a y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.036 |
|
|
\[
{}y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+\left (a +b -1\right ) x y^{\prime }-b y a = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.043 |
|
|
\[
{}y^{\prime \prime \prime }+x^{2 c -2} y^{\prime }+\left (c -1\right ) x^{2 c -3} y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.066 |
|
|
\[
{}y^{\prime \prime \prime }-\left (6 k^{2} \sin \left (x \right )^{2}+a \right ) y^{\prime }+b y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.068 |
|
|
\[
{}y^{\prime \prime \prime }+2 f \left (x \right ) y^{\prime }+f^{\prime }\left (x \right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.045 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime }+10 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.061 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-a^{2} y^{\prime }+2 a^{2} y-\sinh \left (x \right ) = 0
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.732 |
|
|
\[
{}y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y-{\mathrm e}^{a x} = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.127 |
|
|
\[
{}y^{\prime \prime \prime }+\operatorname {a2} y^{\prime \prime }+\operatorname {a1} y^{\prime }+\operatorname {a0} y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.164 |
|
|
\[
{}y^{\prime \prime \prime }-6 x y^{\prime \prime }+2 \left (4 x^{2}+2 a -1\right ) y^{\prime }-8 y a x = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.046 |
|
|
\[
{}y^{\prime \prime \prime }+3 a x y^{\prime \prime }+3 a^{2} x^{2} y^{\prime }+a^{3} x^{3} y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.041 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime } \sin \left (x \right )-2 y^{\prime } \cos \left (x \right )+y \sin \left (x \right )-\ln \left (x \right ) = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.401 |
|
|
\[
{}y^{\prime \prime \prime }+f \left (x \right ) y^{\prime \prime }+y^{\prime }+f \left (x \right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.037 |
|
|
\[
{}y^{\prime \prime \prime }+f \left (x \right ) \left (x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y\right ) = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.046 |
|
|
\[
{}4 y^{\prime \prime \prime }-8 y^{\prime \prime }-11 y^{\prime }-3 y+18 \,{\mathrm e}^{x} = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.107 |
|
|
\[
{}x y^{\prime \prime \prime }+3 y^{\prime \prime }+x y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.035 |
|
|
\[
{}x y^{\prime \prime \prime }+3 y^{\prime \prime }-a \,x^{2} y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.040 |
|
|
\[
{}x y^{\prime \prime \prime }+\left (a +b \right ) y^{\prime \prime }-x y^{\prime }-a y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.042 |
|
|
\[
{}x y^{\prime \prime \prime }-\left (x +2 v \right ) y^{\prime \prime }-\left (x -2 v -1\right ) y^{\prime }+\left (-1+x \right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.040 |
|
|
\[
{}x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-f \left (x \right ) = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.244 |
|
|
\[
{}2 x y^{\prime \prime \prime }+3 y^{\prime \prime }+y a x -b = 0
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.037 |
|
|
\[
{}2 x y^{\prime \prime \prime }-4 \left (x +\nu -1\right ) y^{\prime \prime }+\left (2 x +6 \nu -5\right ) y^{\prime }+\left (1-2 \nu \right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.043 |
|
|
\[
{}2 x y^{\prime \prime \prime }+3 \left (2 a x +k \right ) y^{\prime \prime }+6 \left (a k +b x \right ) y^{\prime }+\left (3 b k +2 c x \right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.047 |
|
|
\[
{}\left (-2+x \right ) x y^{\prime \prime \prime }-\left (-2+x \right ) x y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.517 |
|
|
\[
{}\left (2 x -1\right ) y^{\prime \prime \prime }-8 x y^{\prime }+8 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.037 |
|
|
\[
{}\left (2 x -1\right ) y^{\prime \prime \prime }+\left (x +4\right ) y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.369 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-6 y^{\prime }+a \,x^{2} y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.042 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+\left (x +1\right ) y^{\prime \prime }-y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.038 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-x y^{\prime \prime }+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.330 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+3 x y^{\prime \prime }+\left (4 a^{2} x^{2 a}+1-4 \nu ^{2} a^{2}\right ) y^{\prime } = 4 a^{3} x^{2 a -1} y
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.673 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-3 \left (x -m \right ) x y^{\prime \prime }+\left (2 x^{2}+4 \left (n -m \right ) x +m \left (2 m -1\right )\right ) y^{\prime }-2 n \left (2 x -2 m +1\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.054 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+4 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }+3 x y-f \left (x \right ) = 0
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.040 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime }-\ln \left (x \right ) = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.206 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime }+6 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.178 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime }+6 y^{\prime }+a \,x^{2} y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.042 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-3 \left (p +q \right ) x y^{\prime \prime }+3 p \left (3 q +1\right ) y^{\prime }-x^{2} y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.042 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-2 \left (n +1\right ) x y^{\prime \prime }+\left (a \,x^{2}+6 n \right ) y^{\prime }-2 y a x = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.043 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-\left (x^{2}-2 x \right ) y^{\prime \prime }-\left (x^{2}+\nu ^{2}-\frac {1}{4}\right ) y^{\prime }+\left (x^{2}-2 x +\nu ^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.046 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-\left (x +\nu \right ) x y^{\prime \prime }+\nu \left (2 x +1\right ) y^{\prime }-\nu \left (x +1\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.049 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-2 \left (x^{2}-x \right ) y^{\prime \prime }+\left (x^{2}-2 x +\frac {1}{4}-\nu ^{2}\right ) y^{\prime }+\left (\nu ^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.047 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-\left (x^{4}-6 x \right ) y^{\prime \prime }-\left (2 x^{3}-6\right ) y^{\prime }+2 x^{2} y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.046 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime \prime }+8 x y^{\prime \prime }+10 y^{\prime }-3+\frac {1}{x^{2}}-2 \ln \left (x \right ) = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.299 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime \prime }-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }-2 x y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.039 |
|
|
\[
{}2 x \left (-1+x \right ) y^{\prime \prime \prime }+3 \left (2 x -1\right ) y^{\prime \prime }+\left (2 a x +b \right ) y^{\prime }+a y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.047 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+\left (-\nu ^{2}+1\right ) x y^{\prime }+\left (a \,x^{3}+\nu ^{2}-1\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.045 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+\left (4 x^{3}+\left (-4 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (4 \nu ^{2}-1\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.042 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+\left (a \,x^{2 \nu }+1-\nu ^{2}\right ) x y^{\prime }+\left (b \,x^{3 \nu }+a \left (\nu -1\right ) x^{2 \nu }+\nu ^{2}-1\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.076 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-6 x^{3} \left (-1+x \right ) \ln \left (x \right )+x^{3} \left (x +8\right ) = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.348 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+\left (-a^{2}+1\right ) x y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.181 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+\left (x^{2}+8\right ) x y^{\prime }-2 \left (x^{2}+4\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.046 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+\left (a \,x^{3}-12\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.203 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 \left (1-a \right ) x^{2} y^{\prime \prime }+\left (4 b^{2} c^{2} x^{2 c +1}+1-4 \nu ^{2} c^{2}+3 a \left (a -1\right ) x \right ) y^{\prime }+\left (4 b^{2} c^{2} \left (c -a \right ) x^{2 c}+a \left (4 \nu ^{2} c^{2}-a^{2}\right )\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.095 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+\left (x +3\right ) x^{2} y^{\prime \prime }+5 \left (x -6\right ) x y^{\prime }+\left (4 x +30\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.043 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+\ln \left (x \right )+2 x y^{\prime }-y-2 x^{3} = 0
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
16.108 |
|
|
\[
{}\left (x^{2}+1\right ) x y^{\prime \prime \prime }+3 \left (2 x^{2}+1\right ) y^{\prime \prime }-12 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.044 |
|
|
\[
{}\left (x +3\right ) x^{2} y^{\prime \prime \prime }-3 x \left (x +2\right ) y^{\prime \prime }+6 \left (x +1\right ) y^{\prime }-6 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.045 |
|
|
\[
{}2 \left (x -\operatorname {a1} \right ) \left (x -\operatorname {a2} \right ) \left (x -\operatorname {a3} \right ) y^{\prime \prime \prime }+\left (9 x^{2}-6 \left (\operatorname {a1} +\operatorname {a2} +\operatorname {a3} \right ) x +3 \operatorname {a1} \operatorname {a2} +3 \operatorname {a1} \operatorname {a3} +3 \operatorname {a2} \operatorname {a3} \right ) y^{\prime \prime }-2 \left (\left (n^{2}+n -3\right ) x +b \right ) y^{\prime }-n \left (n +1\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.056 |
|
|
\[
{}\left (x +1\right ) x^{3} y^{\prime \prime \prime }-\left (4 x +2\right ) x^{2} y^{\prime \prime }+\left (10 x +4\right ) x y^{\prime }-4 \left (3 x +1\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.049 |
|
|
\[
{}4 x^{4} y^{\prime \prime \prime }-4 x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }-1 = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.328 |
|
|
\[
{}\left (x^{2}+1\right ) x^{3} y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-4 \left (3 x^{2}+1\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.053 |
|
|
\[
{}x^{6} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.037 |
|
|
\[
{}x^{6} y^{\prime \prime \prime }+6 x^{5} y^{\prime \prime }+a y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.037 |
|
|
\[
{}x^{2} \left (x^{4}+2 x^{2}+2 x +1\right ) y^{\prime \prime \prime }-\left (2 x^{6}+3 x^{4}-6 x^{2}-6 x -1\right ) y^{\prime \prime }+\left (x^{6}-6 x^{3}-15 x^{2}-12 x -2\right ) y^{\prime }+\left (x^{4}+4 x^{3}+8 x^{2}+6 x +1\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.060 |
|
|
\[
{}\left (x -a \right )^{3} \left (x -b \right )^{3} y^{\prime \prime \prime }-c y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.049 |
|
|
\[
{}y^{\prime \prime \prime } \sin \left (x \right )+\left (2 \cos \left (x \right )+1\right ) y^{\prime \prime }-y^{\prime } \sin \left (x \right )-\cos \left (x \right ) = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.642 |
|
|
\[
{}\left (\sin \left (x \right )+x \right ) y^{\prime \prime \prime }+3 \left (\cos \left (x \right )+1\right ) y^{\prime \prime }-3 y^{\prime } \sin \left (x \right )-y \cos \left (x \right )+\sin \left (x \right ) = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.381 |
|
|
\[
{}y^{\prime \prime \prime } \sin \left (x \right )^{2}+3 y^{\prime \prime } \sin \left (x \right ) \cos \left (x \right )+\left (\cos \left (2 x \right )+4 \nu \left (\nu +1\right ) \sin \left (x \right )^{2}\right ) y^{\prime }+2 \nu \left (\nu +1\right ) y \sin \left (2 x \right ) = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.076 |
|
|
\[
{}y^{\prime \prime \prime }+x y^{\prime }+n y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.035 |
|
|
\[
{}y^{\prime \prime \prime }-x y^{\prime }-n y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.036 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.045 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y-f = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.100 |
|
|
\[
{}y^{\prime \prime \prime \prime }+\lambda y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.065 |
|