|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y y^{\prime }-a \left (\frac {n +2}{n}+b \,x^{n}\right ) y = -\frac {a^{2} x \left (\frac {n +1}{n}+b \,x^{n}\right )}{n}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.447 |
|
|
\[
{}y y^{\prime } = \left (a \,{\mathrm e}^{x}+b \right ) y+c \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}-b^{2}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.388 |
|
|
\[
{}y y^{\prime } = \left (a \left (2 \mu +\lambda \right ) {\mathrm e}^{\lambda x}+b \right ) {\mathrm e}^{\mu x} y+\left (-a^{2} \mu \,{\mathrm e}^{2 \lambda x}-a b \,{\mathrm e}^{\lambda x}+c \right ) {\mathrm e}^{2 \mu x}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.982 |
|
|
\[
{}y y^{\prime } = \left (a \,{\mathrm e}^{\lambda x}+b \right ) y+c \left (a^{2} {\mathrm e}^{2 \lambda x}+a b \left (\lambda x +1\right ) {\mathrm e}^{\lambda x}+b^{2} \lambda x \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.906 |
|
|
\[
{}y y^{\prime } = {\mathrm e}^{\lambda x} \left (2 a \lambda x +a +b \right ) y-{\mathrm e}^{2 \lambda x} \left (a^{2} \lambda \,x^{2}+a b x +c \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.660 |
|
|
\[
{}y y^{\prime } = {\mathrm e}^{a x} \left (2 a \,x^{2}+b +2 x \right ) y+{\mathrm e}^{2 a x} \left (-a \,x^{4}-b \,x^{2}+c \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.216 |
|
|
\[
{}y y^{\prime }+a \left (2 b x +1\right ) {\mathrm e}^{b x} y = -a^{2} b \,x^{2} {\mathrm e}^{2 b x}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.201 |
|
|
\[
{}y y^{\prime }-a \left (1+2 n +2 n \left (n +1\right ) x \right ) {\mathrm e}^{\left (n +1\right ) x} y = -a^{2} n \left (n +1\right ) \left (n x +1\right ) x \,{\mathrm e}^{2 \left (n +1\right ) x}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.051 |
|
|
\[
{}y y^{\prime }+a \left (1+2 b \sqrt {x}\right ) {\mathrm e}^{2 b \sqrt {x}} y = -a^{2} b \,x^{{3}/{2}} {\mathrm e}^{4 b \sqrt {x}}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.423 |
|
|
\[
{}y y^{\prime } = \left (a \cosh \left (x \right )+b \right ) y-a b \sinh \left (x \right )+c
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
5.021 |
|
|
\[
{}y y^{\prime } = \left (a \sinh \left (x \right )+b \right ) y-a b \cosh \left (x \right )+c
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
5.580 |
|
|
\[
{}y y^{\prime } = \left (2 \ln \left (x \right )+a +1\right ) y+x \left (-\ln \left (x \right )^{2}-a \ln \left (x \right )+b \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
0.905 |
|
|
\[
{}y y^{\prime } = \left (2 \ln \left (x \right )^{2}+2 \ln \left (x \right )+a \right ) y+x \left (-\ln \left (x \right )^{4}-a \ln \left (x \right )^{2}+b \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.014 |
|
|
\[
{}y y^{\prime } = a x \cos \left (\lambda \,x^{2}\right ) y+x
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.719 |
|
|
\[
{}y y^{\prime } = a x \sin \left (\lambda \,x^{2}\right ) y+x
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.665 |
|
|
\[
{}\left (A y+B x +a \right ) y^{\prime }+B y+k x +b = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.060 |
|
|
\[
{}\left (y+a x +b \right ) y^{\prime } = \alpha y+\beta x +\gamma
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.196 |
|
|
\[
{}\left (y+a k \,x^{2}+b x +c \right ) y^{\prime } = -a y^{2}+2 a k x y+m y+k \left (k +b -m \right ) x +s
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
3.153 |
|
|
\[
{}\left (y+A \,x^{n}+a \right ) y^{\prime }+n A \,x^{n -1} y+k \,x^{m}+b = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
89.677 |
|
|
\[
{}\left (y+a \,x^{n +1}+b \,x^{n}\right ) y^{\prime } = \left (a n \,x^{n}+c \,x^{n -1}\right ) y
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.805 |
|
|
\[
{}x y y^{\prime } = a y^{2}+b y+c \,x^{n}+s
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.879 |
|
|
\[
{}x y y^{\prime } = -n y^{2}+a \left (2 n +1\right ) x y+b y-a^{2} n \,x^{2}-a b x +c
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.090 |
|
|
\[
{}y^{\prime \prime }+a y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.512 |
|
|
\[
{}y^{\prime \prime }-\left (a x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.892 |
|
|
\[
{}y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.868 |
|
|
\[
{}y^{\prime \prime }-\left (a \,x^{2}+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.417 |
|
|
\[
{}y^{\prime \prime }+a^{3} x \left (-a x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.106 |
|
|
\[
{}y^{\prime \prime }-\left (a \,x^{2}+b c x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.381 |
|
|
\[
{}y^{\prime \prime }-a \,x^{n} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.880 |
|
|
\[
{}y^{\prime \prime }-a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.176 |
|
|
\[
{}y^{\prime \prime }-a \,x^{n -2} \left (a \,x^{n}+n +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.161 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.175 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.951 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.667 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }-\left (b \,x^{2}+c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.516 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2}+a x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.285 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b x \left (-b \,x^{3}+a x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.239 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}+a \,x^{n}+n \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
0.361 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.405 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (n -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.401 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 n y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.504 |
|
|
\[
{}y^{\prime \prime }+a x y^{\prime }+b y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.503 |
|
|
\[
{}y^{\prime \prime }+a x y^{\prime }+b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.477 |
|
|
\[
{}y^{\prime \prime }+a x y^{\prime }+\left (b x +c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.547 |
|
|
\[
{}y^{\prime \prime }+2 a x y^{\prime }+\left (b \,x^{4}+a^{2} x^{2}+c x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.541 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.526 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+a y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.255 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (a x +b -c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.303 |
|
|
\[
{}y^{\prime \prime }+\left (a x +2 b \right ) y^{\prime }+\left (a b x +b^{2}-a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.145 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.611 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.226 |
|
|
\[
{}y^{\prime \prime }+2 \left (a x +b \right ) y^{\prime }+\left (a^{2} x^{2}+2 a b x +c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.106 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.276 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (-c \,x^{2 n}+a \,x^{n +1}+b \,x^{n}+n \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.649 |
|
|
\[
{}y^{\prime \prime }+a \left (-b^{2}+x^{2}\right ) y^{\prime }-a \left (x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.433 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c \left (a \,x^{2}+b -c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.401 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{2}+2 b \right ) y^{\prime }+\left (a b \,x^{2}-a x +b^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.451 |
|
|
\[
{}y^{\prime \prime }+\left (2 x^{2}+a \right ) y^{\prime }+\left (x^{4}+a \,x^{2}+b +2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.212 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.623 |
|
|
\[
{}y^{\prime \prime }+\left (a b \,x^{2}+b x +2 a \right ) y^{\prime }+a^{2} \left (b \,x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.583 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+x \left (a b \,x^{2}+b c +2 a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.480 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (a b \,x^{3}+a c \,x^{2}+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.454 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{3}+2 b \right ) y^{\prime }+\left (a b \,x^{3}-a \,x^{2}+b^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.469 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{3}+b x \right ) y^{\prime }+2 \left (2 a \,x^{2}+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.180 |
|
|
\[
{}y^{\prime \prime }+\left (a b \,x^{3}+b \,x^{2}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{3}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.740 |
|
|
\[
{}y^{\prime \prime }+a \,x^{n} y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.967 |
|
|
\[
{}y^{\prime \prime }+a \,x^{n} y^{\prime }+b \,x^{n -1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.622 |
|
|
\[
{}y^{\prime \prime }+2 a \,x^{n} y^{\prime }+a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.147 |
|
|
\[
{}y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (b \,x^{2 n}+c \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.817 |
|
|
\[
{}y^{\prime \prime }+a \,x^{n} y^{\prime }-b \left (a \,x^{n +m}+b \,x^{2 m}+m \,x^{m -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.928 |
|
|
\[
{}y^{\prime \prime }+2 a \,x^{n} y^{\prime }+\left (a^{2} x^{2 n}+b \,x^{2 m}+a n \,x^{n -1}+c \,x^{m -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.047 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}+b -c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.575 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+2 b \right ) y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}+b^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.719 |
|
|
\[
{}y^{\prime \prime }+\left (a b \,x^{n}+b \,x^{n -1}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{n}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.859 |
|
|
\[
{}y^{\prime \prime }+\left (a b \,x^{n}+2 b \,x^{n -1}-a^{2} x \right ) y^{\prime }+a \left (a b \,x^{n}+b \,x^{n -1}-a^{2} x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.311 |
|
|
\[
{}y^{\prime \prime }+x^{n} \left (a \,x^{2}+\left (a c +b \right ) x +b c \right ) y^{\prime }-x^{n} \left (a x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.988 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }-\left (a \,x^{n -1}+b \,x^{m -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.672 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a n \,x^{n -1}+b m \,x^{m -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.103 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a \left (n +1\right ) x^{n -1}+b \left (m +1\right ) x^{m -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.484 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+c \left (a \,x^{n}+b \,x^{m}-c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.852 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a b \,x^{n +m}+b \left (m +1\right ) x^{m -1}-a \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.993 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a b \,x^{n +m}+b c \,x^{m}+a n \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.886 |
|
|
\[
{}x y^{\prime \prime }+\frac {y^{\prime }}{2}+a y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.218 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.884 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.075 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.732 |
|
|
\[
{}x y^{\prime \prime }+n y^{\prime }+b \,x^{1-2 n} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.782 |
|
|
\[
{}x y^{\prime \prime }+\left (1-3 n \right ) y^{\prime }-a^{2} n^{2} x^{2 n -1} y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
0.332 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b \,x^{n} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.065 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b \,x^{n} \left (-b \,x^{n +1}+a +n \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.608 |
|
|
\[
{}x y^{\prime \prime }+a x y^{\prime }+a y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.233 |
|
|
\[
{}x y^{\prime \prime }+\left (b -x \right ) y^{\prime }-a y = 0
\] |
[_Laguerre] |
✗ |
0.732 |
|
|
\[
{}x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.135 |
|
|
\[
{}x y^{\prime \prime }+\left (2 a x +b \right ) y^{\prime }+a \left (a x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.136 |
|
|
\[
{}x y^{\prime \prime }+\left (\left (a +b \right ) x +n +m \right ) y^{\prime }+\left (a b x +a n +b m \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.319 |
|
|
\[
{}x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.681 |
|
|
\[
{}x y^{\prime \prime }-\left (a x +1\right ) y^{\prime }-b \,x^{2} \left (b x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.435 |
|
|
\[
{}x y^{\prime \prime }-\left (2 a x +1\right ) y^{\prime }+\left (b \,x^{3}+a^{2} x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.503 |
|
|
\[
{}x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c x \left (-c \,x^{2}+a x +b +1\right ) = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.114 |
|
|
\[
{}x y^{\prime \prime }-\left (2 a x +1\right ) y^{\prime }+b \,x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.586 |
|