| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10201 |
\begin{align*}
y y^{\prime \prime }&=-{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.705 |
|
| 10202 |
\begin{align*}
\sec \left (\theta \right )^{2}&=\frac {m s^{\prime }}{k} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 10203 |
\begin{align*}
16 y+8 y^{\prime }+y^{\prime \prime }&=x \left (12-{\mathrm e}^{-4 x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 10204 |
\begin{align*}
y_{1}^{\prime }&=-y_{1}-4 y_{2}+4 \\
y_{2}^{\prime }&=y_{1}-y_{2}+1 \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 10205 |
\begin{align*}
y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-8 y_{3} \\
y_{2}^{\prime }&=-4 y_{1}-4 y_{3} \\
y_{3}^{\prime }&=-8 y_{1}-4 y_{2}-6 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 10206 |
\begin{align*}
\left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }&={\mathrm e}^{x} y^{\prime } \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 10207 |
\begin{align*}
y_{1}^{\prime }&=y_{2}-y_{1} \\
y_{2}^{\prime }&=3 y_{1}-4 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 10208 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x +1 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.706 |
|
| 10209 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 x \left (2 x -1\right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.706 |
|
| 10210 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 10211 |
\begin{align*}
y^{\prime \prime }-13 y^{\prime }+36 y&={\mathrm e}^{4 x} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 10212 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 10213 |
\begin{align*}
2 x^{2} \left (2+x \right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 10214 |
\begin{align*}
x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (4 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 10215 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=5 \cos \left (x \right )+10 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 10216 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 10217 |
\begin{align*}
2 \left (1+3 x \right ) y+2 x \left (3 x +2\right ) y^{\prime }+x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.707 |
|
| 10218 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 10219 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 10220 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{10}+25 y&=\cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 10221 |
\begin{align*}
y^{\prime }&=y^{2}-y^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 10222 |
\begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 10223 |
\begin{align*}
y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.707 |
|
| 10224 |
\begin{align*}
y^{\prime \prime } x -x^{2} {y^{\prime }}^{2}+2 y^{\prime }+y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.707 |
|
| 10225 |
\begin{align*}
\left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-3 y^{\prime } {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.707 |
|
| 10226 |
\begin{align*}
{y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.707 |
|
| 10227 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (2 x \right ) \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 10228 |
\begin{align*}
y^{\prime \prime }-k^{2} y&=f \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 10229 |
\begin{align*}
\sin \left (\theta \right )^{2} r^{\prime }&=-b \cos \left (\theta \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 10230 |
\begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 10231 |
\begin{align*}
t^{2} y^{\prime \prime }-t \left (1+t \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 10232 |
\begin{align*}
x^{2} \left (x^{2}+8\right ) y^{\prime \prime }+7 x \left (x^{2}+2\right ) y^{\prime }-\left (-9 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 10233 |
\begin{align*}
y_{1}^{\prime }&=6 y_{1}-5 y_{2}+3 y_{3} \\
y_{2}^{\prime }&=2 y_{1}-y_{2}+3 y_{3} \\
y_{3}^{\prime }&=2 y_{1}+y_{2}+y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 10234 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (-x^{2}+x \right ) y^{\prime }+\left (x^{3}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 10235 |
\begin{align*}
4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 10236 |
\begin{align*}
y^{\prime \prime \prime }-y&=5 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 10237 |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2} \left (1-y^{\prime } \cos \left (y\right )+y y^{\prime } \sin \left (y\right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.708 |
|
| 10238 |
\begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 10239 |
\begin{align*}
y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 10240 |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 10241 |
\begin{align*}
x^{\prime \prime }+x^{\prime }-2 x&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 10242 |
\begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-4 y \\
z^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 10243 |
\begin{align*}
x^{\prime }&=-2 x+y-11 \\
y^{\prime }&=-5 x+4 y-35 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 10244 |
\begin{align*}
y^{\prime \prime }&=x +\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 10245 |
\begin{align*}
y^{\prime \prime }-\frac {\left (-3 x^{2}+x \right ) y^{\prime }}{2 x^{3}+2 x^{2}}+\frac {y}{2 x^{3}+2 x^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| 10246 |
\begin{align*}
3 y+y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.709 |
|
| 10247 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+10 x&={\mathrm e}^{-t} \cos \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| 10248 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&=3+2 \cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| 10249 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=x^{3} {\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| 10250 |
\begin{align*}
2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.709 |
|
| 10251 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (\frac {t}{4}\right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| 10252 |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }+25 y&=100 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 20 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| 10253 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right )^{3} \cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| 10254 |
\begin{align*}
y^{\prime }+3 y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 10255 |
\begin{align*}
\left (1-x \right ) x^{2} y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 10256 |
\begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+9 y^{\prime }-10 y&=10 \,{\mathrm e}^{2 x}+20 \sin \left (2 x \right ) {\mathrm e}^{x}-10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 10257 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 10258 |
\begin{align*}
x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.710 |
|
| 10259 |
\begin{align*}
x \sin \left (x \right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 10260 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+25 y&=-1 \\
y \left (0\right ) &= -{\frac {1}{25}} \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 10261 |
\begin{align*}
x^{\prime }+2 x-3 y&=t \\
y^{\prime }-3 x+2 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 10262 |
\begin{align*}
\left (x -2\right ) y^{\prime \prime }+3 \left (x^{2}-3 x +2\right ) y^{\prime }+\left (x -2\right )^{2} x y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 10263 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\
y \left (2\right ) &= 10 \\
y^{\prime }\left (2\right ) &= 15 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 10264 |
\begin{align*}
3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 10265 |
\begin{align*}
3 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+5 x \left (x^{2}+1\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 10266 |
\begin{align*}
y_{1}^{\prime }&=4 y_{1}-2 y_{2}-2 y_{3} \\
y_{2}^{\prime }&=-2 y_{1}+3 y_{2}-y_{3} \\
y_{3}^{\prime }&=2 y_{1}-y_{2}+3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 10267 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-2 x^{5}+9 x \right ) y^{\prime }+\left (10 x^{4}+5 x^{2}+25\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.711 |
|
| 10268 |
\begin{align*}
2 {y^{\prime }}^{2}-\left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 10269 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=8 \sinh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 10270 |
\begin{align*}
y^{\prime }-2 y x&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 10271 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=3 \sin \left (x \right ) \\
y \left (0\right ) &= -{\frac {9}{10}} \\
y^{\prime }\left (0\right ) &= -{\frac {7}{10}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 10272 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 10273 |
\begin{align*}
y^{\prime \prime } x +\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.711 |
|
| 10274 |
\begin{align*}
\left (1-2 y\right ) {y^{\prime }}^{2}+\left (1+y^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.711 |
|
| 10275 |
\begin{align*}
y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 \,{\mathrm e}^{x} y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.711 |
|
| 10276 |
\begin{align*}
y^{\prime }&=y-\mu y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 10277 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| 10278 |
\begin{align*}
2 y-y^{\prime } x +y^{\prime \prime }&=\cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.712 |
|
| 10279 |
\begin{align*}
x^{\prime }&=3 x-5 y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| 10280 |
\begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| 10281 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }&=\left (3+2 x \right ) \left (4+2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| 10282 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x}+{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| 10283 |
\begin{align*}
y^{\prime }&=x \\
x^{\prime }&=-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| 10284 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| 10285 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-3 x_{2}+{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.713 |
|
| 10286 |
\begin{align*}
y^{\prime \prime } x&=y^{\prime }+{y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.713 |
|
| 10287 |
\begin{align*}
x^{2} y y^{\prime \prime }&=a y^{2}+a x y y^{\prime }+2 x^{2} {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.713 |
|
| 10288 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-8 y&=9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.713 |
|
| 10289 |
\begin{align*}
x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.713 |
|
| 10290 |
\begin{align*}
y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.713 |
|
| 10291 |
\begin{align*}
y^{\prime \prime }+3 y&=x^{2}+1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.713 |
|
| 10292 |
\begin{align*}
y^{\prime \prime }-12 y^{\prime }+36 y&={\mathrm e}^{6 x} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.713 |
|
| 10293 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| 10294 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2}-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| 10295 |
\begin{align*}
t^{2} y^{\prime \prime }-t \left (1+t \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| 10296 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-x_{2} \\
x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\
x_{3}^{\prime }&=6 x_{1}+6 x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| 10297 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-x}+x^{2} \\
\end{align*} |
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✓ |
✓ |
✓ |
0.714 |
|
| 10298 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| 10299 |
\begin{align*}
x^{\prime }-x+y^{\prime }+2 y&=1+{\mathrm e}^{t} \\
y^{\prime }+2 y+z^{\prime }+z&={\mathrm e}^{t}+2 \\
x^{\prime }-x+z^{\prime }+z&=3+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| 10300 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=10 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.714 |
|