| # |
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]] |
✓ |
✓ |
✓ |
✗ |
1.187 |
|
| \begin{align*}
y^{\prime }&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| \begin{align*}
y^{\prime }&=2 \,{\mathrm e}^{3 x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
y^{\prime }&=\frac {2}{\sqrt {-x^{2}+1}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.280 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
y^{\prime }&=\arcsin \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.285 |
|
| \begin{align*}
y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.862 |
|
| \begin{align*}
y^{\prime }&=y^{2} x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.484 |
|
| \begin{align*}
y^{\prime }&=-x \,{\mathrm e}^{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.345 |
|
| \begin{align*}
y^{\prime } \sin \left (y\right )&=x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.391 |
|
| \begin{align*}
y^{\prime } x&=\sqrt {1-y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.215 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \begin{align*}
{y^{\prime }}^{2}-3 y^{\prime }+2&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.246 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.307 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
y^{\prime }&=t^{2}+3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 t} t \\
\end{align*} | [_quadrature] | ✓ | ✓ | ✓ | ✓ | 0.308 |
|
| \begin{align*}
y^{\prime }&=\sin \left (3 t \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.295 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{t^{2}+4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.299 |
|
| \begin{align*}
y^{\prime }&=\ln \left (t \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{\sqrt {t}+1} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
y^{\prime }&=2 y-4 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.142 |
|
| \begin{align*}
y^{\prime }&=-y^{3} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
30.428 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{t}}{y} \\
y \left (\ln \left (2\right )\right ) &= -8 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.097 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 t} t \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right )^{2} \\
y \left (\frac {\pi }{6}\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| \begin{align*}
y^{\prime }&=8 \,{\mathrm e}^{4 t}+t \\
y \left (0\right ) &= 12 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.464 |
|
| \begin{align*}
y^{\prime }&=-\frac {t}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.222 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.182 |
|
| \begin{align*}
y^{\prime }&=y-1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.354 |
|
| \begin{align*}
y^{\prime }&=1-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| \begin{align*}
y^{\prime }&=y^{3}-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.697 |
|
| \begin{align*}
y^{\prime }&=1-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.481 |
|
| \begin{align*}
y^{\prime }&=\left (t^{2}+1\right ) y \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 3.218 |
|
| \begin{align*}
y^{\prime }&=-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.826 |
|
| \begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{-3 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.644 |
|
| \begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{2 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| \begin{align*}
y^{\prime }&=t -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.273 |
|
| \begin{align*}
2 y+t y^{\prime }&=\sin \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.405 |
|
| \begin{align*}
y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.981 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t y}{t^{2}+1}+t +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.025 |
|
| \begin{align*}
y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.058 |
|
| \begin{align*}
y^{\prime }&=y \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| \begin{align*}
y^{\prime }&=2 y \\
y \left (\ln \left (3\right )\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.386 |
|
| \begin{align*}
t y^{\prime }&=y+t^{3} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.253 |
|
| \begin{align*}
y^{\prime }&=-\tan \left (t \right ) y+\sec \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.158 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{t +1} \\
y \left (0\right ) &= 6 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.356 |
|
| \begin{align*}
t y^{\prime }&=-y+t^{3} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.435 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
3.687 |
|
| \begin{align*}
t \ln \left (t \right ) y^{\prime }&=t \ln \left (t \right )-y \\
y \left ({\mathrm e}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.139 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{-t^{2}+1}+3 \\
y \left (\frac {1}{2}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.947 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
2.999 |
|
| \begin{align*}
y^{\prime }-x y^{3}&=0 \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 6.106 |
|
| \begin{align*}
\frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.194 |
|
| \begin{align*}
x^{2} y^{\prime }+x y^{2}&=4 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.241 |
|
| \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]‘]] |
✓ |
✓ |
✓ |
✓ |
3.250 |
|
| \begin{align*}
2 y^{\prime } x +3 x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.274 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
6.024 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+4 y x&=\left (-x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
8.280 |
|
| \begin{align*}
y^{\prime }-\cot \left (x \right ) y+\frac {1}{\sin \left (x \right )}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.437 |
|
| \begin{align*}
\left (y^{3}+x \right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
4.257 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 x^{2}+y^{2}+x}{y x} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.782 |
|
| \begin{align*}
\left (y-x \right ) y^{\prime }+2 x +3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.307 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x +2 y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.316 |
|
| \begin{align*}
y^{\prime }&=-\frac {x +y}{3 x +3 y-4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.812 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
4.504 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
5.303 |
|
| \begin{align*}
y^{\prime }+\frac {x y}{a^{2}+x^{2}}&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.746 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y^{2}}{x^{2}}-y^{2} \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 3.333 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=1 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.492 |
|
| \begin{align*}
y^{\prime }-\tan \left (x \right ) y&=1 \\
y \left (\frac {\pi }{4}\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.037 |
|
| \begin{align*}
y^{\prime }-\frac {y^{2}}{x^{2}}&={\frac {1}{4}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.211 |
|
| \begin{align*}
y^{\prime }-\frac {y^{2}}{x^{2}}&={\frac {1}{4}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.599 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }+2 y \cos \left (x \right )&=1 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.947 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
26.985 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
12.043 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✗ |
10.802 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
11.617 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
6.769 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.370 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.575 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=4 \,{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \begin{align*}
y^{\prime \prime \prime }-12 y^{\prime }+16 y&=32 x -8 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \begin{align*}
\frac {y^{\prime \prime }}{y}-\frac {{y^{\prime }}^{2}}{y^{2}}+\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]] | ✗ | ✓ | ✓ | ✗ | 4.215 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.036 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.982 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.391 |
|
| \begin{align*}
y^{\prime \prime }-y&=x^{n} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.652 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=2 x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.069 |
|
| \begin{align*}
x y^{\prime \prime \prime }+2 y^{\prime \prime }&=A x \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.892 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
0.572 |
|