| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 13001 |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+\left (x^{2}+x -6\right ) y&=0 \\
\end{align*}
Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.932 |
|
| 13002 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.932 |
|
| 13003 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (2 x \right )^{2}+\sin \left (\frac {x}{2}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.932 |
|
| 13004 |
\begin{align*}
x^{\prime }&=8 x-5 y \\
y^{\prime }&=16 x+8 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.932 |
|
| 13005 |
\begin{align*}
x^{\prime }+2 x-y&=100 \sin \left (t \right ) \\
y^{\prime }-4 x-y&=36 t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -8 \\
y \left (0\right ) &= -21 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.932 |
|
| 13006 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+\frac {y}{16}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.932 |
|
| 13007 |
\begin{align*}
m y^{\prime \prime }+b y^{\prime }+k y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.932 |
|
| 13008 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.933 |
|
| 13009 |
\begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.933 |
|
| 13010 |
\begin{align*}
13 y+5 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.933 |
|
| 13011 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{2}+2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.933 |
|
| 13012 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=-18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.933 |
|
| 13013 |
\begin{align*}
x^{\prime }-x&=\frac {t}{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.933 |
|
| 13014 |
\begin{align*}
12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| 13015 |
\begin{align*}
y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| 13016 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x} \cos \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| 13017 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=5 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| 13018 |
\begin{align*}
4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.934 |
|
| 13019 |
\begin{align*}
y^{\prime \prime }&=-\frac {y^{\prime }}{x}-\frac {y}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| 13020 |
\begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-5 \left (x -1\right ) y^{\prime }+9 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.934 |
|
| 13021 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=\tan \left (2 t \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| 13022 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=2 x \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.934 |
|
| 13023 |
\begin{align*}
y+y^{\prime }&=\operatorname {Heaviside}\left (-2+t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| 13024 |
\begin{align*}
x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (4 x +3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| 13025 |
\begin{align*}
x^{2} \left (6+x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| 13026 |
\begin{align*}
-\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.935 |
|
| 13027 |
\begin{align*}
\arctan \left (y x \right )+\frac {y x -2 x y^{2}}{1+y^{2} x^{2}}+\frac {\left (x^{2}-2 x^{2} y\right ) y^{\prime }}{1+y^{2} x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.935 |
|
| 13028 |
\begin{align*}
\left (x +1\right ) y^{\prime \prime }-3 y^{\prime } x +2 y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| 13029 |
\begin{align*}
x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| 13030 |
\begin{align*}
y^{\prime }&=\left (a +b x +y\right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.935 |
|
| 13031 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| 13032 |
\begin{align*}
y^{\prime }-\sqrt {\frac {a y^{2}+b y+c}{a \,x^{2}+b x +c}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.935 |
|
| 13033 |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}+f \left (x \right ) y^{2}+a&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.935 |
|
| 13034 |
\begin{align*}
x^{\prime }&=x+3 z \\
y^{\prime }&=-y \\
z^{\prime }&=-3 x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| 13035 |
\begin{align*}
4 {y^{\prime }}^{2} x^{2} \left (x -1\right )-4 y^{\prime } x y \left (4 x -3\right )+\left (16 x -9\right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| 13036 |
\begin{align*}
y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.936 |
|
| 13037 |
\begin{align*}
t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.936 |
|
| 13038 |
\begin{align*}
-\left (-4 x^{2}+3\right ) y-4 y^{\prime } x +y^{\prime \prime }&={\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.936 |
|
| 13039 |
\begin{align*}
x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-y^{\prime } x +y&=x \left (1-\ln \left (x \right )\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.937 |
|
| 13040 |
\begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x -\left (4 x^{2}+12 x +3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.937 |
|
| 13041 |
\begin{align*}
x^{\prime }&=y-z \\
y^{\prime }&=x+y \\
z^{\prime }&=x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| 13042 |
\begin{align*}
y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -3 \pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| 13043 |
\begin{align*}
x_{1}^{\prime }&=\frac {4 x_{1}}{3}+\frac {4 x_{2}}{3}-\frac {11 x_{3}}{3} \\
x_{2}^{\prime }&=-\frac {16 x_{1}}{3}-\frac {x_{2}}{3}+\frac {14 x_{3}}{3} \\
x_{3}^{\prime }&=3 x_{1}-2 x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| 13044 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| 13045 |
\begin{align*}
x^{\prime }&=-10 x+y+7 z \\
y^{\prime }&=-9 x+4 y+5 z \\
z^{\prime }&=-17 x+y+12 z \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.937 |
|
| 13046 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| 13047 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2}-1 \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| 13048 |
\begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| 13049 |
\begin{align*}
x^{\prime \prime }-2 x^{\prime }&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| 13050 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| 13051 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| 13052 |
\(\left [\begin {array}{ccc} 0 & 1 & 0 \\ -1 & 0 & 1-i \\ 0 & -1-i & 0 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.938 |
|
| 13053 |
\begin{align*}
x^{2} y^{\prime \prime \prime }&={y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| 13054 |
\begin{align*}
b y+2 x^{2} \left (a +x \right ) y^{\prime }+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.939 |
|
| 13055 |
\begin{align*}
x^{\prime }-2 x+y^{\prime }-2 y&=1 \\
y^{\prime }+z^{\prime }+z&=2 \\
3 x+z^{\prime }+z&=3 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| 13056 |
\begin{align*}
y \left (y x +2 y^{2} x^{2}\right )+x \left (y x -y^{2} x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.940 |
|
| 13057 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \cos \left (2 x \right )+\sin \left (2 x \right )+2 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.940 |
|
| 13058 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| 13059 |
\begin{align*}
y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=x^{2} {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.941 |
|
| 13060 |
\begin{align*}
-\left (4 x^{2}+1\right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| 13061 |
\begin{align*}
y^{\prime }-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| 13062 |
\begin{align*}
y^{\prime \prime } x +x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.941 |
|
| 13063 |
\begin{align*}
y^{\prime \prime }+y&=f \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| 13064 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| 13065 |
\begin{align*}
x^{2} \left (x^{2}-1\right )^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.941 |
|
| 13066 |
\begin{align*}
y^{\prime \prime }&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| 13067 |
\begin{align*}
4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+4 \sin \left (2 x \right ) \\
y \left (\pi \right ) &= 2 \pi \\
y^{\prime }\left (\pi \right ) &= 2 \pi \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| 13068 |
\begin{align*}
{y^{\prime }}^{2}-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| 13069 |
\begin{align*}
4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.942 |
|
| 13070 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.942 |
|
| 13071 |
\begin{align*}
y+y^{\prime }&=\delta \left (t -1\right )-\delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.942 |
|
| 13072 |
\begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.942 |
|
| 13073 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= {\mathrm e} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.942 |
|
| 13074 |
\begin{align*}
y^{\prime \prime }&=\frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (a \left (1+a \right )-a \,x^{2} \left (a +3\right )\right ) y}{x^{2} \left (x^{2}-1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.943 |
|
| 13075 |
\begin{align*}
x^{\prime }-3 x-6 y&=9-9 t \\
y^{\prime }+3 x+3 y&=9 t \,{\mathrm e}^{-3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| 13076 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{2}-4 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-4 x_{2}+2 x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| 13077 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+\sqrt {2}\, x_{2}+{\mathrm e}^{-t} \\
x_{2}^{\prime }&=\sqrt {2}\, x_{1}-2 x_{2}-{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| 13078 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=x^{3} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.944 |
|
| 13079 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| 13080 |
\begin{align*}
y^{\prime \prime }&=\operatorname {f3} \left (x \right )+\operatorname {f2} \left (x \right ) y^{2}+\left (\operatorname {f1} \left (x \right )-2 y\right ) y^{\prime } \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.944 |
|
| 13081 |
\begin{align*}
{y^{\prime }}^{2}-y^{2} a^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| 13082 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| 13083 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| 13084 |
\begin{align*}
y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (-1+a \right ) b +a \,x^{2}+\left (1-a \right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.944 |
|
| 13085 |
\begin{align*}
x^{\prime }&=4 x-13 y \\
y^{\prime }&=2 x-6 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| 13086 |
\begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{r}&=4-4 r \\
u \left (1\right ) &= 15 \\
u^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.944 |
|
| 13087 |
\begin{align*}
z^{\prime }+4 i z&={\mathrm e}^{8 i t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| 13088 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2}-x_{3} \\
x_{3}^{\prime }&=-x_{1}+2 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| 13089 |
\begin{align*}
4 {y^{\prime }}^{2}+2 x \,{\mathrm e}^{-2 y} y^{\prime }-{\mathrm e}^{-2 y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.945 |
|
| 13090 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x&=1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| 13091 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-2 y-5 z+3 \\
z^{\prime }&=y+2 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.945 |
|
| 13092 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| 13093 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| 13094 |
\begin{align*}
\left (a \,x^{2}+2 b x +c \right ) y^{\prime \prime }+3 \left (a x +b \right ) y^{\prime }+d y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.946 |
|
| 13095 |
\begin{align*}
z^{\prime }+y+3 z&={\mathrm e}^{x} \\
y^{\prime }+3 y+4 z&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| 13096 |
\begin{align*}
y^{\prime \prime } x +\left (2 x -1\right ) y^{\prime }&=-4 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.946 |
|
| 13097 |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.947 |
|
| 13098 |
\begin{align*}
y^{\prime }+2 y&=1 \\
y \left (0\right ) &= {\frac {5}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| 13099 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| 13100 |
\begin{align*}
y^{\prime \prime }&=-\frac {y^{\prime }}{x +1}-\frac {y}{x \left (x +1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.947 |
|