| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 9201 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.609 |
|
| 9202 |
\begin{align*}
y^{\prime }&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.609 |
|
| 9203 |
\begin{align*}
x_{1}^{\prime }&=28 x_{1}+50 x_{2}+100 x_{3} \\
x_{2}^{\prime }&=15 x_{1}+33 x_{2}+60 x_{3} \\
x_{3}^{\prime }&=-15 x_{1}-30 x_{2}-57 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| 9204 |
\begin{align*}
y y^{\prime \prime }&={\mathrm e}^{x} y \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+{\mathrm e}^{2 x} \left (\operatorname {a2} +\operatorname {a3} y^{4}\right )+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.610 |
|
| 9205 |
\begin{align*}
y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| 9206 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.610 |
|
| 9207 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.610 |
|
| 9208 |
\begin{align*}
6 y+18 y^{\prime } x +9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.610 |
|
| 9209 |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }&=8 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| 9210 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| 9211 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=\cosh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| 9212 |
\begin{align*}
2 y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{x} \left (x^{2}-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| 9213 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| 9214 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| 9215 |
\begin{align*}
y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y&=0 \\
y \left (-1\right ) &= 0 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*} Series expansion around \(t=-1\). |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| 9216 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=5 \sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| 9217 |
\begin{align*}
y^{\prime \prime }-9 y&=x +{\mathrm e}^{2 x}-\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| 9218 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=-4 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| 9219 |
\begin{align*}
y^{\prime } x +y&=2 x^{4}+x^{3}+x \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.611 |
|
| 9220 |
\begin{align*}
1&=\left (x^{2}-9\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| 9221 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| 9222 |
\begin{align*}
9 \left (x +3\right ) x^{2} y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (4 x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 9223 |
\begin{align*}
\left (1-x \right )^{2} x^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 9224 |
\begin{align*}
2 y^{\prime \prime }-y^{\prime }+3 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 9225 |
\begin{align*}
3 y^{\prime \prime }+4 y^{\prime }+y&=\sin \left (t \right ) {\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 9226 |
\begin{align*}
y^{\prime \prime }-4 y&=\frac {8}{{\mathrm e}^{2 x}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 9227 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-x_{2}-2 x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{3} \\
x_{3}^{\prime }&=x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 9228 |
\begin{align*}
x^{\prime \prime }-x&=\frac {1}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 9229 |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 9230 |
\begin{align*}
y^{\prime \prime }+y&=6 \cos \left (x \right )-3 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 9231 |
\begin{align*}
\sin \left (x \right ) y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=\frac {\pi }{2}\). |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 9232 |
\begin{align*}
z^{\prime \prime }-4 z&=\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 9233 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 9234 |
\begin{align*}
x^{\prime }&=5 x-6 y \\
y^{\prime }&=6 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 9235 |
\begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y&=\sin \left (x \right )-{\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| 9236 |
\begin{align*}
y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| 9237 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \sec \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| 9238 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (-v^{2}+x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| 9239 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+y^{\prime } x -y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| 9240 |
\begin{align*}
y^{\prime \prime }+y&=2 x -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| 9241 |
\begin{align*}
6 y^{\prime \prime }+11 y^{\prime }+4 y&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| 9242 |
\begin{align*}
x^{\prime }-x+y&=2 \sin \left (t \right ) \\
x^{\prime }+y^{\prime }&=3 y-3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 9243 |
\begin{align*}
9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 9244 |
\begin{align*}
2 y^{\prime \prime } x +y^{\prime }-2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 9245 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 9246 |
\begin{align*}
2 x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 9247 |
\begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 9248 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-t}-4 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 9249 |
\begin{align*}
y^{\prime } x&=2 x^{2}+1 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 9250 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2}+3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 9251 |
\begin{align*}
y^{\prime }+y&=2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 9252 |
\begin{align*}
y_{1}^{\prime }&=5 y_{1}-y_{2}+y_{3} \\
y_{2}^{\prime }&=-y_{1}+9 y_{2}-3 y_{3} \\
y_{3}^{\prime }&=-2 y_{1}+2 y_{2}+4 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 9253 |
\begin{align*}
y&=y^{\prime } x +\frac {3}{{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.615 |
|
| 9254 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-10 x_{2} \\
x_{2}^{\prime }&=5 x_{1}+11 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 9255 |
\begin{align*}
x^{\prime }&=3 x-4 y \\
y^{\prime }&=4 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 9256 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 9257 |
\begin{align*}
y^{\prime \prime }&=a \sqrt {1+{y^{\prime }}^{2}}+b \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.615 |
|
| 9258 |
\begin{align*}
x^{\prime }&=-6 y \\
y^{\prime }&=6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 9259 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-12 y&=0 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 9260 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (6 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 9261 |
\begin{align*}
y^{\prime }&=\ln \left (x \right ) \\
y \left ({\mathrm e}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 9262 |
\begin{align*}
4 y+y^{\prime \prime }&={\mathrm e}^{x}+\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 9263 |
\begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 9264 |
\begin{align*}
4 x^{2} \left (4 x^{2}+1\right ) y^{\prime \prime }+32 x^{3} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 9265 |
\begin{align*}
x_{1}^{\prime }&=10 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+2 x_{2}+\frac {{\mathrm e}^{6 t}}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 9266 |
\begin{align*}
x^{\prime }-2 x-y&=2 \,{\mathrm e}^{t} \\
y^{\prime }-2 y-4 z&=4 \,{\mathrm e}^{2 t} \\
x-z^{\prime }-z&=0 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 9 \\
y \left (0\right ) &= 3 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 9267 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.616 |
|
| 9268 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 9269 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 9270 |
\begin{align*}
y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 9271 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.616 |
|
| 9272 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {\left (-2 x^{2}+1\right ) y}{4 x^{6}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.616 |
|
| 9273 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&=5 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 9274 |
\begin{align*}
y^{\prime } x&=\sin \left (x \right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 9275 |
\begin{align*}
x^{\prime \prime }&=-20 \\
x \left (0\right ) &= 5 \\
x^{\prime }\left (0\right ) &= -15 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 9276 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }+\left (12 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 9277 |
\begin{align*}
2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 9278 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 9279 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 9280 |
\(\left [\begin {array}{cc} 7 & -2 \\ 26 & -1 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.617 |
|
| 9281 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 9282 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 9283 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 9284 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}-16} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 9285 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} \sqrt {-t^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 9286 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }&={\mathrm e}^{4 x} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 9287 |
\begin{align*}
4 t^{2} x^{\prime \prime }+4 t x^{\prime }-x&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 9288 |
\begin{align*}
t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y&={\mathrm e}^{2 t} t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.618 |
|
| 9289 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=x_{2}-8 x_{3} \\
x_{3}^{\prime }&=2 x_{2}-7 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| 9290 |
\begin{align*}
\left (a +x \right ) y^{\prime }&=b x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| 9291 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| 9292 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| 9293 |
\begin{align*}
y^{\prime \prime }+i y^{\prime }+2 y&=2 \cosh \left (2 x \right )+{\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| 9294 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
y^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| 9295 |
\begin{align*}
t^{2} y+y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| 9296 |
\begin{align*}
y^{\prime \prime }-\frac {2 y}{x^{2}}&=x \,{\mathrm e}^{-\sqrt {x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| 9297 |
\begin{align*}
x^{\prime }+y^{\prime }-y&={\mathrm e}^{t} \\
2 x^{\prime }+y^{\prime }+2 y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| 9298 |
\begin{align*}
y^{\prime \prime }+9 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| 9299 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| 9300 |
\begin{align*}
y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.619 |
|