|
# |
ODE |
Mathematica |
Maple |
|
\[
{}\left (3-x \right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-a x y^{\prime }+a^{2} \left (x -1\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (2 x^{3}-a \right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 x y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 x y^{\prime }+4 x^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+n^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x} = n^{2} y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{3}+6 x^{2}+4\right ) y = 0
\] |
✗ |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-\left (a^{2}+1\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\left (n^{2}+\frac {2}{x^{2}}\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 n \cot \left (n x \right ) y^{\prime }+\left (m^{2}-n^{2}\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {y \left (-8+\sqrt {x}+x \right )}{4 x^{2}} = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 n x y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}} = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+m^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-\sin \left (x \right )^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime \prime }+\cos \left (x \right ) \sin \left (x \right ) y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (\tan \left (x \right )-1\right )^{2} y^{\prime }-n \left (n -1\right ) y \sec \left (x \right )^{4} = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (3 \sin \left (x \right )-\cot \left (x \right )\right ) y^{\prime }+2 \sin \left (x \right )^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+2\right ) y^{\prime }-4 y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }-y = \left (x -1\right ) \left (y^{\prime \prime }-x +1\right )
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}+a \right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\left (n^{2}+\frac {2}{x^{2}}\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a} = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\frac {a^{2} y}{-x^{2}+1} = 0
\] |
✓ |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) \left (3 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{3}-2 x^{2}\right ) y^{\prime \prime }+2 x^{2} y^{\prime }-12 \left (x -2\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime } \left (x \cos \left (x \right )-2 \sin \left (x \right )\right )+\left (x^{2}+2\right ) y^{\prime } \sin \left (x \right )-2 \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y = 0
\] |
✗ |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime } = m^{2} y
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime \prime } = 2 y
\] |
✓ |
✓ |
|
|
\[
{}\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 \left (x^{2}+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+\frac {\csc \left (x \right )^{2} y}{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+6 x +2\right ) y^{\prime }-4 y = 0
\] |
✓ |
✓ |
|