|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.281 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
40.152 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.723 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }-\left (b \,x^{2}+c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.614 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2}+a x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.378 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b x \left (-b \,x^{3}+a x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.294 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}+a \,x^{n}+n \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
0.561 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.523 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (n -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.547 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 n y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.526 |
|
|
\[
{}y^{\prime \prime }+a x y^{\prime }+b y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.605 |
|
|
\[
{}y^{\prime \prime }+a x y^{\prime }+b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.584 |
|
|
\[
{}y^{\prime \prime }+a x y^{\prime }+\left (b x +c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.656 |
|
|
\[
{}y^{\prime \prime }+2 a x y^{\prime }+\left (b \,x^{4}+a^{2} x^{2}+c x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.671 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.522 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+a y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.440 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (a x +b -c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.451 |
|
|
\[
{}y^{\prime \prime }+\left (a x +2 b \right ) y^{\prime }+\left (a b x +b^{2}-a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.193 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.759 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.380 |
|
|
\[
{}y^{\prime \prime }+2 \left (a x +b \right ) y^{\prime }+\left (a^{2} x^{2}+2 a b x +c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
136.241 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.372 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (-c \,x^{2 n}+a \,x^{n +1}+b \,x^{n}+n \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.809 |
|
|
\[
{}y^{\prime \prime }+a \left (-b^{2}+x^{2}\right ) y^{\prime }-a \left (x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.571 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c \left (a \,x^{2}+b -c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.588 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{2}+2 b \right ) y^{\prime }+\left (a b \,x^{2}-a x +b^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.618 |
|
|
\[
{}y^{\prime \prime }+\left (2 x^{2}+a \right ) y^{\prime }+\left (x^{4}+a \,x^{2}+b +2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
80.414 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.812 |
|
|
\[
{}y^{\prime \prime }+\left (a b \,x^{2}+b x +2 a \right ) y^{\prime }+a^{2} \left (b \,x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.746 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+x \left (a b \,x^{2}+b c +2 a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.648 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (a b \,x^{3}+a c \,x^{2}+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.559 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{3}+2 b \right ) y^{\prime }+\left (a b \,x^{3}-a \,x^{2}+b^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.652 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{3}+b x \right ) y^{\prime }+2 \left (2 a \,x^{2}+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.231 |
|
|
\[
{}y^{\prime \prime }+\left (a b \,x^{3}+b \,x^{2}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{3}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.784 |
|
|
\[
{}y^{\prime \prime }+a \,x^{n} y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.026 |
|
|
\[
{}y^{\prime \prime }+a \,x^{n} y^{\prime }+b \,x^{n -1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.757 |
|
|
\[
{}y^{\prime \prime }+2 a \,x^{n} y^{\prime }+a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.192 |
|
|
\[
{}y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (b \,x^{2 n}+c \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.898 |
|
|
\[
{}y^{\prime \prime }+a \,x^{n} y^{\prime }-b \left (a \,x^{n +m}+b \,x^{2 m}+m \,x^{m -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.082 |
|
|
\[
{}y^{\prime \prime }+2 a \,x^{n} y^{\prime }+\left (a^{2} x^{2 n}+b \,x^{2 m}+a n \,x^{n -1}+c \,x^{m -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.187 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}+b -c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.685 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+2 b \right ) y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}+b^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.793 |
|
|
\[
{}y^{\prime \prime }+\left (a b \,x^{n}+b \,x^{n -1}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{n}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.022 |
|
|
\[
{}y^{\prime \prime }+\left (a b \,x^{n}+2 b \,x^{n -1}-a^{2} x \right ) y^{\prime }+a \left (a b \,x^{n}+b \,x^{n -1}-a^{2} x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.425 |
|
|
\[
{}y^{\prime \prime }+x^{n} \left (a \,x^{2}+\left (a c +b \right ) x +b c \right ) y^{\prime }-x^{n} \left (a x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.125 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }-\left (a \,x^{n -1}+b \,x^{m -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.683 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a n \,x^{n -1}+b m \,x^{m -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.181 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a \left (n +1\right ) x^{n -1}+b \left (m +1\right ) x^{m -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.200 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+c \left (a \,x^{n}+b \,x^{m}-c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.939 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a b \,x^{n +m}+b \left (m +1\right ) x^{m -1}-a \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.090 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a b \,x^{n +m}+b c \,x^{m}+a n \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.042 |
|
|
\[
{}x y^{\prime \prime }+\frac {y^{\prime }}{2}+a y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.644 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.003 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.099 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.819 |
|
|
\[
{}x y^{\prime \prime }+n y^{\prime }+b \,x^{1-2 n} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.228 |
|
|
\[
{}x y^{\prime \prime }+\left (1-3 n \right ) y^{\prime }-a^{2} n^{2} x^{2 n -1} y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
0.500 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b \,x^{n} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.125 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b \,x^{n} \left (-b \,x^{n +1}+a +n \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.717 |
|
|
\[
{}x y^{\prime \prime }+a x y^{\prime }+a y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.315 |
|
|
\[
{}x y^{\prime \prime }+\left (b -x \right ) y^{\prime }-a y = 0
\] |
[_Laguerre] |
✗ |
0.862 |
|
|
\[
{}x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.271 |
|
|
\[
{}x y^{\prime \prime }+\left (2 a x +b \right ) y^{\prime }+a \left (a x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.186 |
|
|
\[
{}x y^{\prime \prime }+\left (\left (a +b \right ) x +n +m \right ) y^{\prime }+\left (a b x +a n +b m \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.432 |
|
|
\[
{}x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y = 0
\] |
[[_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]] |
✓ |
1.470 |
|
|
\[
{}x y^{\prime \prime }-\left (2 a x +1\right ) y^{\prime }+\left (b \,x^{3}+a^{2} x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.608 |
|
|
\[
{}x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c x \left (-c \,x^{2}+a x +b +1\right ) = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.316 |
|
|
\[
{}x y^{\prime \prime }-\left (2 a x +1\right ) y^{\prime }+b \,x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.675 |
|
|
\[
{}x y^{\prime \prime }+\left (a b \,x^{2}+b -5\right ) y^{\prime }+2 a^{2} \left (b -2\right ) x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.452 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }-\left (a c \,x^{2}+\left (b c +c^{2}+a \right ) x +b +2 c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.756 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{2}+b x +2\right ) y^{\prime }+b y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.664 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (2 a x +b \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.871 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (c -1\right ) \left (a x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.480 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (A \,x^{2}+B x +\operatorname {C0} \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.073 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{2}+b x +2\right ) y^{\prime }+\left (c \,x^{2}+d x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.910 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{3}+b \right ) y^{\prime }+a \left (b -1\right ) x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.595 |
|
|
\[
{}x y^{\prime \prime }+x \left (a \,x^{2}+b \right ) y^{\prime }+\left (3 a \,x^{2}+b \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.541 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{3}+b \,x^{2}+2\right ) y^{\prime }+b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.832 |
|
|
\[
{}x y^{\prime \prime }+\left (a b \,x^{3}+b \,x^{2}+a x -1\right ) y^{\prime }+a^{2} b \,x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.903 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime }+\left (d -1\right ) \left (a \,x^{2}+b x +c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.641 |
|
|
\[
{}x y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}-b^{2} x +2 b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.868 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{n}+2\right ) y^{\prime }+a \,x^{n -1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.888 |
|
|
\[
{}x y^{\prime \prime }+\left (x^{n}+1-n \right ) y^{\prime }+b \,x^{2 n -1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.662 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+a n \,x^{n -1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.952 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+a \left (b -1\right ) x^{n -1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.985 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+a \left (b +n -1\right ) x^{n -1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.412 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}-c x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.853 |
|
|
\[
{}x y^{\prime \prime }+\left (a b \,x^{n}+b -3 n +1\right ) y^{\prime }+a^{2} n \left (b -n \right ) x^{2 n -1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.896 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+\left (c \,x^{2 n -1}+d \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.857 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b \,x^{n -1}+2\right ) y^{\prime }+b \,x^{n -2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.945 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b x \right ) y^{\prime }+\left (a b \,x^{n}+a n \,x^{n -1}-b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.776 |
|
|
\[
{}x y^{\prime \prime }+\left (a b \,x^{n}+b \,x^{n -1}+a x -1\right ) y^{\prime }+a^{2} b \,x^{n} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.281 |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (c -1\right ) \left (a \,x^{n -1}+b \,x^{m -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.602 |
|
|
\[
{}x y^{\prime \prime }+\left (a b \,x^{n +m}+a n \,x^{n}+b \,x^{m}+1-2 n \right ) y^{\prime }+a^{2} b n \,x^{2 n +m -1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.398 |
|
|
\[
{}\left (x +a \right ) y^{\prime \prime }+\left (b x +c \right ) y^{\prime }+b y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.633 |
|
|
\[
{}\left (a_{1} x +a_{0} \right ) y^{\prime \prime }+\left (b_{1} x +b_{0} \right ) y^{\prime }-m b_{1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.270 |
|
|
\[
{}\left (a x +b \right ) y^{\prime \prime }+s \left (c x +d \right ) y^{\prime }-s^{2} \left (\left (a +c \right ) x +b +d \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.738 |
|
|
\[
{}\left (a_{2} x +b_{2} \right ) y^{\prime \prime }+\left (a_{1} x +b_{1} \right ) y^{\prime }+\left (a_{0} x +b_{0} \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
6.015 |
|
|
\[
{}\left (x +\gamma \right ) y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a n \,x^{n -1}+b m \,x^{m -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.471 |
|