| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10101 |
\begin{align*}
x^{\prime }&={\mathrm e}^{t}-y-5 x \\
y^{\prime }&={\mathrm e}^{2 t}+x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= {\frac {119}{900}} \\
y \left (0\right ) &= {\frac {211}{900}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| 10102 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\
x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10103 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}} \\
y \left (1\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10104 |
\begin{align*}
z y^{\prime \prime }-2 y^{\prime }+y z&=0 \\
\end{align*}
Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10105 |
\begin{align*}
x \left (-y x +1\right ) \left (1-x^{2} y^{2}\right ) y^{\prime }+\left (y x +1\right ) \left (1+x^{2} y^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10106 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10107 |
\begin{align*}
2 x y^{\prime \prime }+y^{\prime }-x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10108 |
\begin{align*}
y^{\prime \prime }+2 x y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10109 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=1+\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.757 |
|
| 10110 |
\begin{align*}
s^{\prime \prime }-a^{2} s&=t +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10111 |
\begin{align*}
y^{\prime }&=2 \sin \left (x \right ) \\
y \left (\pi \right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10112 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=\left (12 x -7\right ) {\mathrm e}^{-x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10113 |
\begin{align*}
x^{\prime }+x&=2 \sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10114 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }+y x&=x +2 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.757 |
|
| 10115 |
\begin{align*}
y&=x y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10116 |
\begin{align*}
y^{\prime \prime }-9 y&={\mathrm e}^{-3 x} \left (x^{2}+\sin \left (3 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10117 |
\begin{align*}
\left (2 x +1\right ) y^{\prime \prime }+4 x y^{\prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.757 |
|
| 10118 |
\begin{align*}
2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-3 x +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| 10119 |
\begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{3}+\frac {y_{2}}{3}-y_{3} \\
y_{2}^{\prime }&=-\frac {4 y_{1}}{3}-\frac {4 y_{2}}{3}+y_{3} \\
y_{3}^{\prime }&=-\frac {2 y_{1}}{3}+\frac {y_{2}}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| 10120 |
\begin{align*}
-y+y^{\prime }&=2 \cos \left (5 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| 10121 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| 10122 |
\begin{align*}
x y^{\prime \prime }&=y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| 10123 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+3 x_{2}+8 \\
x_{2}^{\prime }&=x_{1}+5 x_{2}+4 \,{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| 10124 |
\begin{align*}
x y^{\prime \prime }-2 \left (1+\tan \left (x \right )^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.758 |
|
| 10125 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=5 x_{2}-7 x_{3} \\
x_{3}^{\prime }&=2 x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 10126 |
\begin{align*}
y^{\prime }&=a x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 10127 |
\begin{align*}
y^{\prime \prime }+\frac {2 {y^{\prime }}^{2}}{1-y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.759 |
|
| 10128 |
\begin{align*}
3 y^{\prime \prime }+5 y^{\prime }-2 y&=3 t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 10129 |
\begin{align*}
x^{\prime }&=x-5 y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 10130 |
\begin{align*}
y^{\prime \prime }-2 k y^{\prime }+k^{2} y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 10131 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}-2 x_{3}+3 x_{4} \\
x_{2}^{\prime }&=2 x_{1}-\frac {3 x_{2}}{2}-x_{3}+\frac {7 x_{4}}{2} \\
x_{3}^{\prime }&=-x_{1}+\frac {x_{2}}{2}-\frac {3 x_{4}}{2} \\
x_{4}^{\prime }&=-2 x_{1}+\frac {3 x_{2}}{2}+3 x_{3}-\frac {7 x_{4}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 10132 |
\begin{align*}
y^{\prime \prime }+2 p y^{\prime }+\left (p^{2}+q^{2}\right ) y&={\mathrm e}^{k x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 10133 |
\begin{align*}
4 y+y^{\prime \prime }&=4 \sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 10134 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-4 x^{2}+3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10135 |
\begin{align*}
y^{\prime \prime }+9 y&=2 \sec \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10136 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-4 x_{2} \\
x_{2}^{\prime }&=-8 x_{1}+4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10137 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\sin \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10138 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }&={\mathrm e}^{x} x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10139 |
\begin{align*}
u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.760 |
|
| 10140 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=4 \sqrt {x}\, {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.760 |
|
| 10141 |
\begin{align*}
\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2}&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10142 |
\begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=7 x+4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 6 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10143 |
\begin{align*}
x^{\prime \prime }+6 x^{\prime }+10 x&=0 \\
x \left (0\right ) &= 3 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10144 |
\begin{align*}
y_{1}^{\prime }&=y_{1}+2 y_{2}+x -1 \\
y_{2}^{\prime }&=3 y_{1}+2 y_{2}-5 x -2 \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -2 \\
y_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10145 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\delta \left (-4+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10146 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+29 y&={\mathrm e}^{-2 t} \sin \left (5 t \right ) \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10147 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10148 |
\begin{align*}
{y^{\prime }}^{2}-a \,x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10149 |
\begin{align*}
x^{\prime }&=5 x+4 y+2 z \\
y^{\prime }&=4 x+5 y+2 z \\
z^{\prime }&=2 x+2 y+2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10150 |
\begin{align*}
t^{2} x^{\prime \prime }+3 x^{\prime } t&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10151 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=-2 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10152 |
\begin{align*}
x^{\prime }+x+y^{\prime }+y&=0 \\
x^{\prime }-y^{\prime }-y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10153 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10154 |
\begin{align*}
y^{\prime \prime }-4 y&=-7 \,{\mathrm e}^{2 x}+x \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10155 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.761 |
|
| 10156 |
\begin{align*}
y^{\prime \prime }-2 a y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.761 |
|
| 10157 |
\begin{align*}
y^{\prime \prime }+y&=2 \,{\mathrm e}^{x}+x^{3}-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10158 |
\begin{align*}
x^{\prime \prime }-x^{\prime }+x&=\sin \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10159 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{5}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10160 |
\begin{align*}
y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\left (1+\sin \left (x \right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.761 |
|
| 10161 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10162 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{2} \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10163 |
\begin{align*}
y_{1}^{\prime }&=-2 y_{1}-12 y_{2}+10 y_{3} \\
y_{2}^{\prime }&=2 y_{1}-24 y_{2}+11 y_{3} \\
y_{3}^{\prime }&=2 y_{1}-24 y_{2}+8 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10164 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10165 |
\begin{align*}
\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2}&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10166 |
\begin{align*}
4 x^{2} y^{\prime \prime }+y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10167 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y&=8 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -3 \\
y^{\prime \prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10168 |
\begin{align*}
y^{\prime }&=\frac {1}{x -1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10169 |
\begin{align*}
x^{\prime }&=t +y \\
y^{\prime }&=x-t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10170 |
\begin{align*}
i^{\prime \prime }+2 i^{\prime }+5 i&=0 \\
i \left (0\right ) &= 2 \\
i^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10171 |
\begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=\sin \left (x \right )+\cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10172 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10173 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10174 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}-8 \\
x_{2}^{\prime }&=x_{1}+x_{2}+3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10175 |
\begin{align*}
y^{\prime \prime }-2 i y^{\prime }-y&={\mathrm e}^{i x}-2 \,{\mathrm e}^{-i x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10176 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=\cos \left (x \right )+\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.763 |
|
| 10177 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=\left (1+\sin \left (x \right )\right ) {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10178 |
\begin{align*}
x^{\prime }&=x+2 y+2 t \\
y^{\prime }&=3 y+t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10179 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10180 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10181 |
\begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y&=2 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.763 |
|
| 10182 |
\begin{align*}
t y^{\prime \prime }+\left (2-5 t \right ) y^{\prime }+\left (6 t -5\right ) y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.763 |
|
| 10183 |
\begin{align*}
h y^{2}+\operatorname {g1} y y^{\prime }+\operatorname {g0} {y^{\prime }}^{2}+\operatorname {f2} y y^{\prime \prime }+\operatorname {f1} y^{\prime } y^{\prime \prime }+\operatorname {f0} {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.764 |
|
| 10184 |
\begin{align*}
y^{\prime \prime }&=-\frac {a y}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| 10185 |
\begin{align*}
y^{\prime \prime }+4 y&=\tan \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| 10186 |
\begin{align*}
y^{\prime \prime }-y \,{\mathrm e}^{x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| 10187 |
\begin{align*}
4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| 10188 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }+y x&=x +2 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.764 |
|
| 10189 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| 10190 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{3} \\
x_{2}^{\prime }&=2 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{3} \\
x_{4}^{\prime }&=-x_{3}+2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| 10191 |
\begin{align*}
x^{\prime \prime }+x^{\prime } t&=t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| 10192 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-5\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.765 |
|
| 10193 |
\begin{align*}
x^{\prime }&=-5 x-y+2 \\
y^{\prime }&=3 x-y-3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| 10194 |
\begin{align*}
{\mathrm e}^{y^{\prime }}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| 10195 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\pi ^{2}-x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| 10196 |
\begin{align*}
x^{4} \left ({y^{\prime }}^{2}-2 y y^{\prime \prime }\right )&=4 x^{3} y y^{\prime }+1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.765 |
|
| 10197 |
\begin{align*}
t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 y t&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10198 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=F \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10199 |
\begin{align*}
-2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x \left (x^{2}+3\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10200 |
\begin{align*}
y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.766 |
|