| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y&=x^{2} \left (x +1\right )^{2} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.141 |
|
| \begin{align*}
y^{\prime }&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
y^{\prime }&=2 \,{\mathrm e}^{3 x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.400 |
|
| \begin{align*}
y^{\prime }&=\frac {2}{\sqrt {-x^{2}+1}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
y^{\prime }&=\arcsin \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.906 |
|
| \begin{align*}
y^{\prime }&=y^{2} x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.286 |
|
| \begin{align*}
y^{\prime }&=-x \,{\mathrm e}^{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.316 |
|
| \begin{align*}
y^{\prime } \sin \left (y\right )&=x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.505 |
|
| \begin{align*}
y^{\prime } x&=\sqrt {1-y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.134 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.387 |
|
| \begin{align*}
{y^{\prime }}^{2}-3 y^{\prime }+2&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.284 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \begin{align*}
y^{\prime }&=t^{2}+3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 t} t \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| \begin{align*}
y^{\prime }&=\sin \left (3 t \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.399 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{t^{2}+4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
y^{\prime }&=\ln \left (t \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.374 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{\sqrt {t}+1} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.427 |
|
| \begin{align*}
y^{\prime }&=2 y-4 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| \begin{align*}
y^{\prime }&=-y^{3} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
66.491 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{t}}{y} \\
y \left (\ln \left (2\right )\right ) &= -8 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.415 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 t} t \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right )^{2} \\
y \left (\frac {\pi }{6}\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
y^{\prime }&=8 \,{\mathrm e}^{4 t}+t \\
y \left (0\right ) &= 12 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.505 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.661 |
|
| \begin{align*}
y^{\prime }&=-\frac {t}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.856 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| \begin{align*}
y^{\prime }&=y-1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.397 |
|
| \begin{align*}
y^{\prime }&=1-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \begin{align*}
y^{\prime }&=y^{3}-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.541 |
|
| \begin{align*}
y^{\prime }&=1-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.750 |
|
| \begin{align*}
y^{\prime }&=\left (t^{2}+1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.228 |
|
| \begin{align*}
y^{\prime }&=-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| \begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{-3 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.728 |
|
| \begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{2 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.414 |
|
| \begin{align*}
y^{\prime }&=t -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.363 |
|
| \begin{align*}
2 y+y^{\prime } t&=\sin \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.515 |
|
| \begin{align*}
y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.001 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t y}{t^{2}+1}+t +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.967 |
|
| \begin{align*}
y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.351 |
|
| \begin{align*}
y^{\prime }&=y \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.312 |
|
| \begin{align*}
y^{\prime }&=2 y \\
y \left (\ln \left (3\right )\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.594 |
|
| \begin{align*}
y^{\prime } t&=y+t^{3} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.620 |
|
| \begin{align*}
y^{\prime }&=-\tan \left (t \right ) y+\sec \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.200 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{1+t} \\
y \left (0\right ) &= 6 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.612 |
|
| \begin{align*}
y^{\prime } t&=-y+t^{3} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.612 |
|
| \begin{align*}
y^{\prime }+4 \tan \left (2 t \right ) y&=\tan \left (2 t \right ) \\
y \left (\frac {\pi }{8}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.294 |
|
| \begin{align*}
t \ln \left (t \right ) y^{\prime }&=t \ln \left (t \right )-y \\
y \left ({\mathrm e}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.444 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{-t^{2}+1}+3 \\
y \left (\frac {1}{2}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| \begin{align*}
y^{\prime }&=-\cot \left (t \right ) y+6 \cos \left (t \right )^{2} \\
y \left (\frac {\pi }{4}\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.921 |
|
| \begin{align*}
y^{\prime }-x y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.547 |
|
| \begin{align*}
\frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.024 |
|
| \begin{align*}
x^{2} y^{\prime }+x y^{2}&=4 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.212 |
|
| \begin{align*}
y \left (2 y^{2} x^{2}+1\right ) y^{\prime }+x \left (1+y^{4}\right )&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
2.998 |
|
| \begin{align*}
2 y^{\prime } x +3 x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
19.123 |
|
| \begin{align*}
\left (\cos \left (x \right )^{2}+y \sin \left (2 x \right )\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
6.729 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+4 y x&=\left (-x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
15.795 |
|
| \begin{align*}
y^{\prime }-\cot \left (x \right ) y+\frac {1}{\sin \left (x \right )}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.332 |
|
| \begin{align*}
\left (y^{3}+x \right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
5.244 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 x^{2}+y^{2}+x}{y x} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.741 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }+2 x +3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.491 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x +2 y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.086 |
|
| \begin{align*}
y^{\prime }&=-\frac {x +y}{3 x +3 y-4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.615 |
|
| \begin{align*}
y^{\prime }&=\tan \left (x \right ) \cos \left (y\right ) \left (\cos \left (y\right )+\sin \left (y\right )\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.671 |
|
| \begin{align*}
x \left (1-2 x^{2} y\right ) y^{\prime }+y&=3 y^{2} x^{2} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
5.894 |
|
| \begin{align*}
y^{\prime }+\frac {x y}{a^{2}+x^{2}}&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
18.398 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y^{2}}{x^{2}}-y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.403 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=1 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.957 |
|
| \begin{align*}
y^{\prime }-\tan \left (x \right ) y&=1 \\
y \left (\frac {\pi }{4}\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.184 |
|
| \begin{align*}
y^{\prime }-\frac {y^{2}}{x^{2}}&={\frac {1}{4}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.903 |
|
| \begin{align*}
y^{\prime }-\frac {y^{2}}{x^{2}}&={\frac {1}{4}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.987 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }+2 \cos \left (x \right ) y&=1 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.084 |
|
| \begin{align*}
\left (5 x +y-7\right ) y^{\prime }&=3 x +3 y+3 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
43.211 |
|
| \begin{align*}
y^{\prime } x +y-\frac {y^{2}}{x^{{3}/{2}}}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.059 |
|
| \begin{align*}
\left (2 \sin \left (y\right )-x \right ) y^{\prime }&=\tan \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
17.620 |
|
| \begin{align*}
\left (2 \sin \left (y\right )-x \right ) y^{\prime }&=\tan \left (y\right ) \\
y \left (0\right ) &= \frac {\pi }{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
19.130 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}+y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
5.219 |
|
| \begin{align*}
x^{\prime \prime }+\omega _{0}^{2} x&=a \cos \left (\omega t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
78.402 |
|
| \begin{align*}
f^{\prime \prime }+2 f^{\prime }+5 f&=0 \\
f \left (0\right ) &= 1 \\
f^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
7.253 |
|
| \begin{align*}
f^{\prime \prime }+2 f^{\prime }+5 f&={\mathrm e}^{-t} \cos \left (3 t \right ) \\
f \left (0\right ) &= 0 \\
f^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
6.178 |
|
| \begin{align*}
f^{\prime \prime }+6 f^{\prime }+9 f&={\mathrm e}^{-t} \\
f \left (0\right ) &= 0 \\
f^{\prime }\left (0\right ) &= \lambda \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
61.238 |
|
| \begin{align*}
f^{\prime \prime }+8 f^{\prime }+12 f&=12 \,{\mathrm e}^{-4 t} \\
f \left (0\right ) &= 0 \\
f^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.089 |
|
| \begin{align*}
f^{\prime \prime }+8 f^{\prime }+12 f&=12 \,{\mathrm e}^{-4 t} \\
f \left (0\right ) &= 0 \\
f^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.604 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=4 \,{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
15.651 |
|
| \begin{align*}
y^{\prime \prime \prime }-12 y^{\prime }+16 y&=32 x -8 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.168 |
|
| \begin{align*}
-\frac {{y^{\prime }}^{2}}{y^{2}}+\frac {y^{\prime \prime }}{y}+\frac {2 a \coth \left (2 a x \right ) y^{\prime }}{y}&=2 a^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
4.914 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.279 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }+y&=x^{2} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
47.602 |
|
| \begin{align*}
\left (x -2\right ) y^{\prime \prime }+3 y^{\prime }+\frac {4 y}{x^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
10.346 |
|
| \begin{align*}
y^{\prime \prime }-y&=x^{n} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
10.161 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=2 x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
19.195 |
|
| \begin{align*}
2 y y^{\prime \prime \prime }+2 \left (y+3 y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}&=\sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear]] |
✗ |
✓ |
✓ |
✗ |
0.076 |
|
| \begin{align*}
x y^{\prime \prime \prime }+2 y^{\prime \prime }&=A x \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+6\right ) y&={\mathrm e}^{-x^{2}} \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
6.223 |
|
| \begin{align*}
\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y&=0 \\
\end{align*} Series expansion around \(z=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.559 |
|