|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{6} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.051 |
|
|
\[
{}x^{6} y^{\prime \prime \prime }+6 x^{5} y^{\prime \prime }+a y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.053 |
|
|
\[
{}x^{2} \left (x^{4}+2 x^{2}+2 x +1\right ) y^{\prime \prime \prime }-\left (2 x^{6}+3 x^{4}-6 x^{2}-6 x -1\right ) y^{\prime \prime }+\left (x^{6}-6 x^{3}-15 x^{2}-12 x -2\right ) y^{\prime }+\left (x^{4}+4 x^{3}+8 x^{2}+6 x +1\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.062 |
|
|
\[
{}\left (x -a \right )^{3} \left (x -b \right )^{3} y^{\prime \prime \prime }-c y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.103 |
|
|
\[
{}y^{\prime \prime \prime } \sin \left (x \right )+\left (2 \cos \left (x \right )+1\right ) y^{\prime \prime }-y^{\prime } \sin \left (x \right )-\cos \left (x \right ) = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
1.259 |
|
|
\[
{}\left (\sin \left (x \right )+x \right ) y^{\prime \prime \prime }+3 \left (\cos \left (x \right )+1\right ) y^{\prime \prime }-3 y^{\prime } \sin \left (x \right )-y \cos \left (x \right )+\sin \left (x \right ) = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✗ |
0.059 |
|
|
\[
{}y^{\prime \prime \prime } \sin \left (x \right )^{2}+3 y^{\prime \prime } \sin \left (x \right ) \cos \left (x \right )+\left (\cos \left (2 x \right )+4 \nu \left (\nu +1\right ) \sin \left (x \right )^{2}\right ) y^{\prime }+2 \nu \left (\nu +1\right ) y \sin \left (2 x \right ) = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.069 |
|
|
\[
{}f^{\prime }\left (x \right ) y^{\prime \prime }+f \left (x \right ) y^{\prime \prime \prime }+g^{\prime }\left (x \right ) y^{\prime }+g \left (x \right ) y^{\prime \prime }+h^{\prime }\left (x \right ) y+h \left (x \right ) y^{\prime }+A \left (x \right ) \left (f \left (x \right ) y^{\prime \prime }+g \left (x \right ) y^{\prime }+h \left (x \right ) y\right ) = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.058 |
|
|
\[
{}y^{\prime \prime \prime }+x y^{\prime }+n y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.049 |
|
|
\[
{}y^{\prime \prime \prime }-x y^{\prime }-n y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.049 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.039 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y-f = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime \prime \prime }+\lambda y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.080 |
|
|
\[
{}y^{\prime \prime \prime \prime }-12 y^{\prime \prime }+12 y-16 x^{4} {\mathrm e}^{x^{2}} = 0
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.194 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y-\cosh \left (a x \right ) = 0
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.063 |
|
|
\[
{}y^{\prime \prime \prime \prime }+\left (\lambda +1\right ) a^{2} y^{\prime \prime }+\lambda \,a^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.113 |
|
|
\[
{}y^{\prime \prime \prime \prime }+a \left (b x -1\right ) y^{\prime \prime }+a b y^{\prime }+\lambda y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.050 |
|
|
\[
{}y^{\prime \prime \prime \prime }+\left (a \,x^{2}+b \lambda +c \right ) y^{\prime \prime }+\left (a \,x^{2}+\beta \lambda +\gamma \right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.050 |
|
|
\[
{}y^{\prime \prime \prime \prime }+a \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime \prime }+b \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime }+\left (c \left (6 \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )^{2}-\frac {\operatorname {g2}}{2}\right )+d \right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.056 |
|
|
\[
{}y^{\prime \prime \prime \prime }-\left (12 k^{2} \operatorname {JacobiSN}\left (z , x\right )^{2}+a \right ) y^{\prime \prime }+b y^{\prime }+\left (\alpha \operatorname {JacobiSN}\left (z , x\right )^{2}+\beta \right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.062 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y-32 \sin \left (2 x \right )+24 \cos \left (2 x \right ) = 0
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.178 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 a x y^{\prime \prime \prime }+6 a^{2} x^{2} y^{\prime \prime }+4 a^{3} x^{3} y^{\prime }+a^{4} x^{4} y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.051 |
|
|
\[
{}4 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+11 y^{\prime \prime }-3 y^{\prime }-4 \cos \left (x \right ) = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.144 |
|
|
\[
{}x y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-24 = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.378 |
|
|
\[
{}x y^{\prime \prime \prime \prime }-\left (6 x^{2}+1\right ) y^{\prime \prime \prime }+12 x^{3} y^{\prime \prime }-\left (9 x^{2}-7\right ) x^{2} y^{\prime }+2 \left (x^{2}-3\right ) x^{3} y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.056 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }-2 \left (\nu ^{2} x^{2}+6\right ) y^{\prime \prime }+\nu ^{2} \left (\nu ^{2} x^{2}+4\right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.061 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }+2 x y^{\prime \prime \prime }+a y-b \,x^{2} = 0
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✗ |
0.056 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }+4 x y^{\prime \prime \prime }+2 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.214 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }+6 x y^{\prime \prime \prime }+6 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.203 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }+6 x y^{\prime \prime \prime }+6 y^{\prime \prime }-\lambda ^{2} y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.049 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.183 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime }-\lambda ^{2} y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.050 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }+\left (2 n -2 \nu +4\right ) x y^{\prime \prime \prime }+\left (n -\nu +1\right ) \left (n -\nu +2\right ) y^{\prime \prime }-\frac {b^{4} y}{16} = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.058 |
|
|
\[
{}x^{3} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime } x^{2}-x y^{\prime \prime }+y^{\prime }-a^{4} x^{3} y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.052 |
|
|
\[
{}x^{3} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime } x^{2}+6 x y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.222 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }-2 n \left (n +1\right ) x^{2} y^{\prime \prime }+4 n \left (n +1\right ) x y^{\prime }+\left (a \,x^{4}+n \left (n +1\right ) \left (3+n \right ) \left (n -2\right )\right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.061 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }+\left (4 n^{2}-1\right ) x y^{\prime }-4 x^{4} y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.086 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }-\left (4 n^{2}-1\right ) x y^{\prime }+\left (-4 x^{4}+4 n^{2}-1\right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.058 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}+3\right ) x^{2} y^{\prime \prime }+\left (12 n^{2}-3\right ) x y^{\prime }-\left (4 x^{4}+12 n^{2}-3\right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.059 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-\rho ^{2}-\sigma ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-\rho ^{2}-\sigma ^{2}+1\right ) x \right ) y^{\prime }+\left (\rho ^{2} \sigma ^{2}+8 x^{2}\right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.055 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-2 \mu ^{2}-2 \nu ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-2 \mu ^{2}-2 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (8 x^{2}+\left (\mu ^{2}-\nu ^{2}\right )^{2}\right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.056 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.135 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }+a y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.161 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a \right ) x^{3} y^{\prime \prime \prime }+\left (4 b^{2} c^{2} x^{2 c}+6 \left (a -1\right )^{2}-2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )+1\right ) x^{2} y^{\prime \prime }+\left (4 \left (3 c -2 a +1\right ) b^{2} c^{2} x^{2 c}+\left (2 a -1\right ) \left (2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )-2 a \left (a -1\right )-1\right )\right ) x y^{\prime }+\left (4 \left (a -c \right ) \left (a -2 c \right ) b^{2} c^{2} x^{2 c}+\left (c \mu +c \nu +a \right ) \left (c \mu +c \nu -a \right ) \left (c \mu -c \nu +a \right ) \left (c \mu -c \nu -a \right )\right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.108 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a -4 c \right ) x^{3} y^{\prime \prime \prime }+\left (-2 \nu ^{2} c^{2}+2 a^{2}+4 \left (a +c -1\right )^{2}+4 \left (a -1\right ) \left (c -1\right )-1\right ) x^{2} y^{\prime \prime }+\left (2 \nu ^{2} c^{2}-2 a^{2}-\left (2 a -1\right ) \left (2 c -1\right )\right ) \left (2 a +2 c -1\right ) x y^{\prime }+\left (\left (-\nu ^{2} c^{2}+a^{2}\right ) \left (-\nu ^{2} c^{2}+a^{2}+4 a c +4 c^{2}\right )-b^{4} c^{4} x^{4 c}\right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.098 |
|
|
\[
{}\nu ^{4} x^{4} y^{\prime \prime \prime \prime }+\left (4 \nu -2\right ) \nu ^{3} x^{3} y^{\prime \prime \prime }+\left (\nu -1\right ) \left (2 \nu -1\right ) \nu ^{2} x^{2} y^{\prime \prime }-\frac {b^{4} x^{\frac {2}{\nu }} y}{16} = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.083 |
|
|
\[
{}\left (x^{2}-1\right )^{2} y^{\prime \prime \prime \prime }+10 x \left (x^{2}-1\right ) y^{\prime \prime \prime }+\left (24 x^{2}-8-2 \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )\right ) \left (x^{2}-1\right )\right ) y^{\prime \prime }-6 x \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )-2\right ) y^{\prime }+\left (\left (\mu \left (\mu +1\right )-\nu \left (\nu +1\right )\right )^{2}-2 \mu \left (\mu +1\right )-2 \nu \left (\nu +1\right )\right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.068 |
|
|
\[
{}\left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \,{\mathrm e}^{x} y^{\prime }+y \,{\mathrm e}^{x}-\frac {1}{x^{5}} = 0
\] |
[[_high_order, _fully, _exact, _linear]] |
✗ |
0.063 |
|
|
\[
{}y^{\prime \prime \prime \prime } \sin \left (x \right )^{4}+2 y^{\prime \prime \prime } \sin \left (x \right )^{3} \cos \left (x \right )+y^{\prime \prime } \sin \left (x \right )^{2} \left (\sin \left (x \right )^{2}-3\right )+y^{\prime } \sin \left (x \right ) \cos \left (x \right ) \left (2 \sin \left (x \right )^{2}+3\right )+\left (a^{4} \sin \left (x \right )^{4}-3\right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.060 |
|
|
\[
{}y^{\prime \prime \prime \prime } \sin \left (x \right )^{6}+4 y^{\prime \prime \prime } \sin \left (x \right )^{5} \cos \left (x \right )-6 y^{\prime \prime } \sin \left (x \right )^{6}-4 y^{\prime } \sin \left (x \right )^{5} \cos \left (x \right )+y \sin \left (x \right )^{6}-f = 0
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✗ |
0.054 |
|
|
\[
{}f \left (y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y\right )+2 \operatorname {df} \left (y^{\prime \prime \prime }-a^{2} y^{\prime }\right ) = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.093 |
|
|
\[
{}f y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.065 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y-\lambda \left (a x -b \right ) \left (y^{\prime \prime }-a^{2} y\right ) = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.056 |
|
|
\[
{}y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime }-a x -b \sin \left (x \right )-c \cos \left (x \right ) = 0
\] |
[[_high_order, _missing_y]] |
✓ |
1.489 |
|
|
\[
{}y^{\left (6\right )}+y-\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right ) = 0
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
2.683 |
|
|
\[
{}y^{\left (5\right )}-a x y-b = 0
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✗ |
0.043 |
|
|
\[
{}y^{\left (5\right )}+a \,x^{\nu } y^{\prime }+a \nu \,x^{\nu -1} y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.052 |
|
|
\[
{}y^{\left (5\right )}+a y^{\prime \prime \prime \prime }-f = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.118 |
|
|
\[
{}x y^{\left (5\right )}-m n y^{\prime \prime \prime \prime }+a x y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.048 |
|
|
\[
{}x \left (a y^{\prime }+b y^{\prime \prime }+c y^{\prime \prime \prime }+e y^{\prime \prime \prime \prime }\right ) y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.442 |
|
|
\[
{}x y^{\left (5\right )}-\left (a A_{1} -A_{0} \right ) x -A_{1} -\left (\left (a A_{2} -A_{1} \right ) x +A_{2} \right ) y^{\prime } = 0
\] |
[[_high_order, _missing_y]] |
✗ |
0.075 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }-a y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.052 |
|
|
\[
{}x^{10} y^{\left (5\right )}-a y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.051 |
|
|
\[
{}x^{{5}/{2}} y^{\left (5\right )}-a y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.066 |
|
|
\[
{}\left (x -a \right )^{5} \left (x -b \right )^{5} y^{\left (5\right )}-c y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.060 |
|
|
\[
{}y^{\prime \prime }-y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.900 |
|
|
\[
{}y^{\prime \prime }-6 y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.843 |
|
|
\[
{}y^{\prime \prime }-6 y^{2}-x = 0
\] |
[[_Painleve, ‘1st‘]] |
✗ |
0.085 |
|
|
\[
{}y^{\prime \prime }-6 y^{2}+4 y = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.741 |
|
|
\[
{}y^{\prime \prime }+y^{2} a +b x +c = 0
\] |
[NONE] |
✗ |
0.090 |
|
|
\[
{}y^{\prime \prime }-2 y^{3}-x y+a = 0
\] |
[[_Painleve, ‘2nd‘]] |
✗ |
0.089 |
|
|
\[
{}y^{\prime \prime }-a y^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.640 |
|
|
\[
{}y^{\prime \prime }-2 a^{2} y^{3}+2 a b x y-b = 0
\] |
[NONE] |
✗ |
0.093 |
|
|
\[
{}y^{\prime \prime }+d +b x y+c y+a y^{3} = 0
\] |
[NONE] |
✗ |
0.093 |
|
|
\[
{}y^{\prime \prime }+d +b y^{2}+c y+a y^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.942 |
|
|
\[
{}y^{\prime \prime }+a \,x^{r} y^{2} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.093 |
|
|
\[
{}y^{\prime \prime }+6 a^{10} y^{11}-y = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.988 |
|
|
\[
{}y^{\prime \prime }-\frac {1}{\left (y^{2} a +b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{{3}/{2}}} = 0
\] |
[NONE] |
✗ |
0.332 |
|
|
\[
{}y^{\prime \prime }-{\mathrm e}^{y} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
35.130 |
|
|
\[
{}y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.124 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right ) = 0
\] |
[NONE] |
✗ |
0.176 |
|
|
\[
{}y^{\prime \prime }+a \sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.201 |
|
|
\[
{}y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right ) = 0
\] |
[NONE] |
✗ |
0.309 |
|
|
\[
{}y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right ) = 0
\] |
[NONE] |
✗ |
0.209 |
|
|
\[
{}y^{\prime \prime } = \frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{{3}/{2}}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.381 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.508 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.092 |
|
|
\[
{}y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
2.198 |
|
|
\[
{}y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
2.394 |
|
|
\[
{}y^{\prime \prime }-\frac {\left (3 n +4\right ) y^{\prime }}{n}-\frac {2 \left (n +1\right ) \left (2+n \right ) y \left (y^{\frac {n}{n +1}}-1\right )}{n^{2}} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.333 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b y^{n}+\frac {\left (a^{2}-1\right ) y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.007 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n} = 0
\] |
[NONE] |
✗ |
0.102 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.789 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right ) = 0
\] |
[NONE] |
✗ |
0.140 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } y-y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
24.017 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } y-y^{3}+a y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
4.575 |
|
|
\[
{}y^{\prime \prime }+\left (y+3 a \right ) y^{\prime }-y^{3}+y^{2} a +2 a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
4.363 |
|
|
\[
{}y^{\prime \prime }+\left (y+3 f \left (x \right )\right ) y^{\prime }-y^{3}+y^{2} f \left (x \right )+y \left (f^{\prime }\left (x \right )+2 f \left (x \right )^{2}\right ) = 0
\] |
[NONE] |
✗ |
0.109 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } y-y^{3}-\left (\frac {f^{\prime }\left (x \right )}{f \left (x \right )}+f \left (x \right )\right ) \left (3 y^{\prime }+y^{2}\right )+\left (a f \left (x \right )^{2}+3 f^{\prime }\left (x \right )+\frac {3 {f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}\right ) y+b f \left (x \right )^{3} = 0
\] |
[NONE] |
✗ |
0.137 |
|
|
\[
{}y^{\prime \prime }+\left (y-\frac {3 f^{\prime }\left (x \right )}{2 f \left (x \right )}\right ) y^{\prime }-y^{3}-\frac {f^{\prime }\left (x \right ) y^{2}}{2 f \left (x \right )}+\frac {\left (f \left (x \right )+\frac {{f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}-f^{\prime \prime }\left (x \right )\right ) y}{2 f \left (x \right )} = 0
\] |
[NONE] |
✗ |
0.133 |
|