| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=\frac {x \arctan \left (x \right )}{y} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.098 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.909 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.488 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1+y^{2}}\, \sin \left (y\right )^{2} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
4.224 |
|
| \begin{align*}
y^{\prime }&=y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.059 |
|
| \begin{align*}
y^{\prime }&=y+\frac {y}{x \ln \left (x \right )} \\
y \left ({\mathrm e}\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.978 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \begin{align*}
y^{\prime }&=\sqrt {\frac {1-y^{2}}{-x^{2}+1}} \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.437 |
|
| \begin{align*}
m^{\prime }&=-\frac {k}{m^{2}} \\
m \left (0\right ) &= m_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✗ |
✓ |
✓ |
6.158 |
|
| \begin{align*}
u^{\prime }&=a \sqrt {1+u^{2}} \\
u \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.774 |
|
| \begin{align*}
x^{\prime }&=k \left (A -x\right )^{2} \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.977 |
|
| \begin{align*}
1+{x^{\prime }}^{2}&=\frac {a}{y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
0.661 |
|
| \begin{align*}
y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
1.036 |
|
| \begin{align*}
y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\
y \left (-1\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
0.963 |
|
| \begin{align*}
y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\
y \left (-1\right ) &= -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
0.647 |
|
| \begin{align*}
\left (2 y+2\right ) y^{\prime }-4 x^{3}-6 x&=0 \\
y \left (0\right ) &= -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.099 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (1-x \right )}{y \left (y-2\right )} \\
y \left (0\right ) &= {\frac {3}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.907 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (1-x \right )}{y \left (y-2\right )} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.564 |
|
| \begin{align*}
y^{\prime }&=5 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
2 y+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| \begin{align*}
3 y^{\prime }+12 y&=4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \begin{align*}
y^{\prime }+3 x^{2} y&=x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.343 |
|
| \begin{align*}
y^{\prime }+2 y x&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.332 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.033 |
|
| \begin{align*}
y^{\prime }&=2 y+x^{2}+5 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.960 |
|
| \begin{align*}
-y+y^{\prime } x&=x^{2} \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.524 |
|
| \begin{align*}
y^{\prime } x +2 y&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.507 |
|
| \begin{align*}
4 y+y^{\prime } x&=x^{3}-x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.444 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-y x&=x^{2}+x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.744 |
|
| \begin{align*}
x^{2} y^{\prime }+x \left (2+x \right ) y&={\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.004 |
|
| \begin{align*}
y^{\prime } x +\left (x +1\right ) y&={\mathrm e}^{-x} \sin \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.467 |
|
| \begin{align*}
y-4 \left (x +y^{6}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
4.999 |
|
| \begin{align*}
y&=\left ({\mathrm e}^{y} y-2 x \right ) y^{\prime } \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
1.933 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.241 |
|
| \begin{align*}
\cos \left (x \right )^{2} \sin \left (x \right ) y^{\prime }+\cos \left (x \right )^{3} y&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.204 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+\left (2+x \right ) y&=2 x \,{\mathrm e}^{-x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.180 |
|
| \begin{align*}
\left (2+x \right )^{2} y^{\prime }&=5-8 y-4 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.683 |
|
| \begin{align*}
r^{\prime }+r \sec \left (t \right )&=\cos \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.241 |
|
| \begin{align*}
p^{\prime }+2 t p&=p+4 t -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.615 |
|
| \begin{align*}
y^{\prime } x +\left (1+3 x \right ) y&={\mathrm e}^{-3 x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.155 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y&=\left (x +1\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.352 |
|
| \begin{align*}
y^{\prime }&=x +5 y \\
y \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.254 |
|
| \begin{align*}
y^{\prime }&=2 x -3 y \\
y \left (0\right ) &= {\frac {1}{3}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.230 |
|
| \begin{align*}
y^{\prime } x +y&={\mathrm e}^{x} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.026 |
|
| \begin{align*}
y y^{\prime }-x&=2 y^{2} \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.657 |
|
| \begin{align*}
L i^{\prime }+R i&=E \\
i \left (0\right ) &= i_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.590 |
|
| \begin{align*}
T^{\prime }&=k \left (T-T_{m} \right ) \\
T \left (0\right ) &= T_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.437 |
|
| \begin{align*}
y^{\prime } x +y&=4 x +1 \\
y \left (1\right ) &= 8 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.197 |
|
| \begin{align*}
y^{\prime }+4 y x&=x^{3} {\mathrm e}^{x^{2}} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.056 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y&=\ln \left (x \right ) \\
y \left (1\right ) &= 10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.081 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime }+y x&=1 \\
y \left ({\mathrm e}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.684 |
|
| \begin{align*}
y^{\prime }-\sin \left (x \right ) y&=2 \sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.026 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right ) y&=\cos \left (x \right )^{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.401 |
|
| \begin{align*}
2 y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le x \le 3 \\ 0 & 3<x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.572 |
|
| \begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} 1 & 0\le x \le 1 \\ -1 & 1<x \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.477 |
|
| \begin{align*}
y^{\prime }+2 y x&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
1.747 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=\left \{\begin {array}{cc} x & 0\le x <1 \\ -x & 1\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
1.284 |
|
| \begin{align*}
y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le x \le 1 \\ -\frac {2}{x} & 1<x \end {array}\right .\right ) y&=4 x \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.661 |
|
| \begin{align*}
y^{\prime }+\left (\left \{\begin {array}{cc} 1 & 0\le x \le 2 \\ 5 & 2<x \end {array}\right .\right ) y&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
3.174 |
|
| \begin{align*}
y^{\prime }-2 y x&=1 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.617 |
|
| \begin{align*}
y^{\prime }-2 y x&=-1 \\
y \left (0\right ) &= \frac {\sqrt {\pi }}{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.542 |
|
| \begin{align*}
y^{\prime }+{\mathrm e}^{x} y&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.884 |
|
| \begin{align*}
x^{2} y^{\prime }-y&=x^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.829 |
|
| \begin{align*}
2 x^{2} y+x^{3} y^{\prime }&=10 \sin \left (x \right ) \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.438 |
|
| \begin{align*}
y^{\prime }-\sin \left (x^{2}\right ) y&=0 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.282 |
|
| \begin{align*}
1&=\left (x +y^{2}\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.006 |
|
| \begin{align*}
y+\left (2 x +y x -3\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.889 |
|
| \begin{align*}
y^{\prime } x -4 y&=x^{6} {\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.816 |
|
| \begin{align*}
y^{\prime } x -4 y&=x^{6} {\mathrm e}^{x} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_linear] |
✗ |
✗ |
✗ |
✗ |
2.557 |
|
| \begin{align*}
y^{\prime } x -4 y&=x^{6} {\mathrm e}^{x} \\
y \left (x_{0} \right ) &= y_{0} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.224 |
|
| \begin{align*}
x^{\prime }&=-\lambda _{1} x \\
y^{\prime }&=\lambda _{1} x-\lambda _{2} y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
e^{\prime }&=-\frac {e}{r c} \\
e \left (4\right ) &= e_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.032 |
|
| \begin{align*}
2 x -1+\left (3 y+7\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.073 |
|
| \begin{align*}
\left (x^{2}-25\right ) y^{\prime \prime }+2 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
\left (x^{2}-25\right ) y^{\prime \prime }+2 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \begin{align*}
\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| \begin{align*}
\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
y^{\prime \prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.271 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.275 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
2 y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Hermite] |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.371 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.373 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.347 |
|
| \begin{align*}
\left (2+x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.374 |
|
| \begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }-\left (-x +2\right ) y^{\prime }+y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
y^{\prime \prime }+\sin \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✗ |
✓ |
✗ |
0.134 |
|
| \begin{align*}
x \left (x +3\right )^{2} y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.927 |
|