| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 13001 |
\begin{align*}
2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| 13002 |
\begin{align*}
\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.784 |
|
| 13003 |
\begin{align*}
\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.784 |
|
| 13004 |
\begin{align*}
x^{\prime }+5 x+y&={\mathrm e}^{t} \\
y^{\prime }-x+3 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| 13005 |
\begin{align*}
\left (2 x^{2}+3 x \right ) y^{\prime \prime }+\left (3+6 x \right ) y^{\prime }+2 y&={\mathrm e}^{x} \left (x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.784 |
|
| 13006 |
\begin{align*}
5 y x +2 y+5+2 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 13007 |
\begin{align*}
\left (2 x^{2}-x \right ) y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+\left (-2 x^{2}+3 x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 13008 |
\begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }-10 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 13009 |
\begin{align*}
t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 13010 |
\begin{align*}
x_{1}^{\prime }&=147 x_{1}+23 x_{2}-202 x_{3} \\
x_{2}^{\prime }&=-90 x_{1}-9 x_{2}+129 x_{3} \\
x_{3}^{\prime }&=90 x_{1}+15 x_{2}-123 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 13011 |
\begin{align*}
y^{\prime \prime \prime }-7 y^{\prime \prime }+20 y^{\prime }-24 y&=-{\mathrm e}^{2 x} \left (\left (13-8 x \right ) \cos \left (2 x \right )-\left (8-4 x \right ) \sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 13012 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=t^{{5}/{2}} {\mathrm e}^{-2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 13013 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 2 & 0\le t \le 3 \\ 3 t -7 & 3<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 13014 |
\begin{align*}
\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y&=x \left (x +1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.786 |
|
| 13015 |
\begin{align*}
\left (x -y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 13016 |
\begin{align*}
y^{\prime \prime } x -\left (a x +1\right ) y^{\prime }-b \,x^{2} \left (b x +a \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.786 |
|
| 13017 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 x \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 13018 | \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.786 |
|
| 13019 |
\begin{align*}
y^{\prime \prime }+\frac {y}{4}&=\sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 13020 |
\begin{align*}
\left (1+{y^{\prime }}^{2}+y y^{\prime \prime }\right )^{2}&=\left (1+{y^{\prime }}^{2}\right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.786 |
|
| 13021 |
\begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 13022 |
\begin{align*}
2 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+\left (3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 13023 |
\begin{align*}
y^{\prime \prime }+4 y&=8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (t -2\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 13024 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 13025 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{3}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.787 |
|
| 13026 |
\begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 13027 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 13028 |
\begin{align*}
x^{\prime \prime }+x&=t \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 13029 |
\begin{align*}
x^{\prime }&=x-y-z \\
y^{\prime }&=y+3 z \\
z^{\prime }&=3 y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 13030 |
\begin{align*}
u^{\prime \prime }+16 u&=0 \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 13031 |
\begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 4 & 0\le t <2 \\ 8 t & 2\le t <\infty \end {array}\right . \\
\end{align*} Using Laplace transform method. |
✓ |
✗ |
✓ |
✓ |
0.787 |
|
| 13032 |
\begin{align*}
x^{2} \left (x^{2}+2 x +1\right ) y^{\prime \prime }+x \left (4 x^{2}+3 x +1\right ) y^{\prime }-x \left (1-2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| 13033 |
\begin{align*}
y_{1}^{\prime }&=y_{1}-y_{2}+2 y_{3} \\
y_{2}^{\prime }&=12 y_{1}-4 y_{2}+10 y_{3} \\
y_{3}^{\prime }&=-6 y_{1}+y_{2}-7 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| 13034 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.788 |
|
| 13035 |
\begin{align*}
2 y^{\prime \prime } x +y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| 13036 |
\begin{align*}
x^{\prime \prime }-2 a x^{\prime }+b x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| 13037 | \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x+y \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.789 |
|
| 13038 |
\begin{align*}
y^{\prime }&=y+y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 13039 |
\begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 13040 |
\begin{align*}
y+2 y^{\prime }&=3 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 13041 |
\begin{align*}
x_{1}^{\prime }&=a x_{1}+5 x_{3} \\
x_{2}^{\prime }&=-x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 13042 |
\begin{align*}
x^{\prime }&=7 x+4 y-4 z \\
y^{\prime }&=4 x-8 y-z \\
z^{\prime }&=-4 x-y-8 z \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 5 \\
z \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| 13043 |
\begin{align*}
t^{3} y^{\prime \prime }+\sin \left (t^{3}\right ) y^{\prime }+t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.790 |
|
| 13044 |
\begin{align*}
x {y^{\prime }}^{2}-y^{\prime } y-2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.790 |
|
| 13045 |
\begin{align*}
\left (-a +1\right ) a y-2 a x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.790 |
|
| 13046 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| 13047 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{2}+x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| 13048 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\frac {3 y^{\prime }}{2+x}+\frac {\left (1-x \right )^{2} y}{x +3}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| 13049 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.791 |
|
| 13050 |
\begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.791 |
|
| 13051 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=4+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.791 |
|
| 13052 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 13053 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+2 y&={\mathrm e}^{x} \left (\left (20+4 x \right ) \cos \left (x \right )-\left (12+12 x \right ) \sin \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 13054 |
\begin{align*}
4 y+y^{\prime \prime }&=\sinh \left (x \right ) \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 13055 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
y \left (-1\right ) &= 2 \\
y^{\prime }\left (-1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 13056 | \begin{align*}
y^{\prime }&=y-x \\
y \left (0\right ) &= 0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.792 |
|
| 13057 |
\begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (\frac {\pi }{4}\right ) &= \sqrt {2} \\
x^{\prime }\left (\frac {\pi }{4}\right ) &= 2 \sqrt {2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| 13058 |
\begin{align*}
y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{-t^{2}} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.793 |
|
| 13059 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 13060 |
\begin{align*}
y^{\prime \prime } x&=x^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 13061 |
\begin{align*}
x_{1}^{\prime }&=-4 x_{1} \\
x_{2}^{\prime }&=2 x_{1}+5 x_{2}-9 x_{3} \\
x_{3}^{\prime }&=5 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 13062 |
\begin{align*}
4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.793 |
|
| 13063 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 13064 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=-\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| 13065 |
\begin{align*}
y^{\prime } y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.794 |
|
| 13066 |
\begin{align*}
4 t^{2} x^{\prime \prime }+4 t x^{\prime }-x&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| 13067 |
\begin{align*}
x^{2} \left (4 x +1\right ) y^{\prime \prime }-x \left (1-4 x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| 13068 |
\begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| 13069 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.795 |
|
| 13070 |
\begin{align*}
x^{\prime }&=\frac {-x+x^{2}}{2 x-1} \\
x \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| 13071 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {2}{3}-3 x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| 13072 |
\begin{align*}
t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=2 t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.796 |
|
| 13073 |
\begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 13074 |
\begin{align*}
x^{2} \left (x +4\right ) y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| 13075 | \begin{align*}
a -y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.796 |
|
| 13076 |
\begin{align*}
3 x y^{2}-12 x^{2} y y^{\prime }+4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}+8 \left (-x^{3}+1\right ) y y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.796 |
|
| 13077 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\sinh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.796 |
|
| 13078 |
\begin{align*}
\left (\cos \left (y\right )-\sin \left (y\right ) y\right ) y^{\prime \prime }-{y^{\prime }}^{2} \left (2 \sin \left (y\right )+y \cos \left (y\right )\right )&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.796 |
|
| 13079 |
\begin{align*}
-{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.796 |
|
| 13080 |
\begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.797 |
|
| 13081 |
\begin{align*}
y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| 13082 |
\begin{align*}
y^{\prime \prime }-2 x^{2} y-x^{4}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.797 |
|
| 13083 |
\begin{align*}
y^{\prime }&=4 y-5 \\
y \left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| 13084 |
\begin{align*}
y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }-4 y&=-{\mathrm e}^{-x} \left (-\sin \left (x \right )+\cos \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.798 |
|
| 13085 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t^{2} & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.798 |
|
| 13086 |
\begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.798 |
|
| 13087 |
\begin{align*}
a b y \left (y-1\right ) y^{\prime \prime }-\left (\left (2 a b -a -b \right ) y+\left (-a +1\right ) b \right ) {y^{\prime }}^{2}+f y \left (y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.798 |
|
| 13088 |
\begin{align*}
4 x^{\prime }-y^{\prime }+3 x&=\sin \left (t \right ) \\
x^{\prime }+y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.798 |
|
| 13089 |
\begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.798 |
|
| 13090 |
\begin{align*}
x^{\prime }&=y+{\mathrm e}^{t} \\
y^{\prime }&=-2 x+3 y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.798 |
|
| 13091 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.798 |
|
| 13092 |
\begin{align*}
x^{2} \left (x^{2}+3 x +3\right ) y^{\prime \prime }+x \left (7 x^{2}+8 x +5\right ) y^{\prime }-\left (-9 x^{2}-2 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 13093 |
\begin{align*}
\left (a \left (a +1\right )+b^{2} x^{2}\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.799 |
|
| 13094 | \begin{align*}
y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 0.799 |
|
| 13095 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 13096 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=g \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.799 |
|
| 13097 |
\begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=5 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 13098 |
\begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| 13099 |
\begin{align*}
x^{\prime }&=y+\textit {f\_1} \left (t \right ) \\
y^{\prime }&=-x+f_{2} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 13100 |
\begin{align*}
-6 y x -y^{\prime }+x \left (x^{2}+2\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.800 |
|