| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12201 |
\begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }+t^{2} y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 12202 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-3 x_{2}+x_{3}+10 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=2 x_{2}+4 x_{3}+6 \,{\mathrm e}^{2 t} \\
x_{3}^{\prime }&=x_{3}-{\mathrm e}^{2 t} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 5 \\
x_{2} \left (0\right ) &= 11 \\
x_{3} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 12203 |
\begin{align*}
x \left (-x y^{\prime }+y\right )^{2}&={y^{\prime }}^{2} x -2 y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 12204 |
\begin{align*}
{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.017 |
|
| 12205 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.018 |
|
| 12206 |
\begin{align*}
\left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-3 y^{\prime } {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.018 |
|
| 12207 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{3} \\
x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3} \\
x_{3}^{\prime }&=-9 x_{1}+4 x_{2}-x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 17 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| 12208 |
\begin{align*}
4 t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| 12209 |
\begin{align*}
y^{\prime \prime }-2 a y^{\prime }+a^{2} y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| 12210 |
\begin{align*}
a y \left (1-y^{n}\right )+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.019 |
|
| 12211 |
\begin{align*}
2 y y^{\prime \prime }&=-a^{2}-4 \left (-x^{2}+b \right ) y^{2}+8 x y^{3}+3 y^{4}+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.019 |
|
| 12212 |
\begin{align*}
\left (-x^{3}+3 x^{2}-6 x +6\right ) y^{\prime \prime }+x \left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.019 |
|
| 12213 |
\begin{align*}
x^{\prime }&=x+y-z \\
y^{\prime }&=y+z-x \\
z^{\prime }&=x-y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| 12214 |
\begin{align*}
x^{\prime \prime }+x&=\cos \left (t \right ) t -\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| 12215 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+\frac {1}{\cos \left (t \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| 12216 |
\begin{align*}
2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| 12217 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{3} \\
x_{2}^{\prime }&=-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=2 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| 12218 |
\begin{align*}
y^{\prime }&=\frac {1}{-3+y} \\
y \left (-1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| 12219 |
\begin{align*}
x^{\prime }&=6 x-7 y+10 \\
y^{\prime }&=x-2 y-2 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| 12220 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| 12221 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\left (-6+x \right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| 12222 |
\begin{align*}
x^{3} \left (y^{\prime }-x \right )&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| 12223 |
\begin{align*}
y^{\prime \prime \prime \prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= \frac {\sqrt {2}}{2} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| 12224 |
\begin{align*}
x \left (1-x \right ) y^{\prime \prime }+y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| 12225 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=f \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| 12226 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| 12227 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.022 |
|
| 12228 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| 12229 |
\begin{align*}
4 y+y^{\prime \prime }&=4 \tan \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| 12230 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.023 |
|
| 12231 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\sqrt {t +1} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.023 |
|
| 12232 |
\begin{align*}
y^{\prime \prime }+9 y&=8 \sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= -1 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.023 |
|
| 12233 |
\begin{align*}
x^{\prime }&=x+2 y+4 \\
y^{\prime }&=-2 x+y-3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.023 |
|
| 12234 |
\begin{align*}
8 x^{2} y^{\prime \prime }-2 x \left (-x^{2}-4 x +3\right ) y^{\prime }+\left (x^{2}+6 x +3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.024 |
|
| 12235 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.024 |
|
| 12236 |
\begin{align*}
x^{\prime }-4 x+3 y&=\sin \left (t \right ) \\
-2 x+y^{\prime }+y&=-2 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.024 |
|
| 12237 |
\begin{align*}
y^{\prime \prime } \left (x +2\right )^{5}&=1 \\
y \left (-1\right ) &= {\frac {1}{12}} \\
y^{\prime }\left (-1\right ) &= -{\frac {1}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.024 |
|
| 12238 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }-18 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.025 |
|
| 12239 |
\begin{align*}
x^{\prime }-y+z&=0 \\
-x+y^{\prime }-y&=t \\
z^{\prime }-x-z&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.025 |
|
| 12240 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=6 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.025 |
|
| 12241 |
\begin{align*}
2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| 12242 |
\begin{align*}
\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| 12243 |
\begin{align*}
y_{1}^{\prime }-y_{2}&=0 \\
4 y_{1}+y_{2}^{\prime }-4 y_{2}-2 y_{3}&=0 \\
-2 y_{1}+y_{2}+y_{3}^{\prime }+y_{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| 12244 |
\begin{align*}
{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.026 |
|
| 12245 |
\begin{align*}
x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.026 |
|
| 12246 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=\sec \left (2 t \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| 12247 |
\begin{align*}
t^{2} y^{\prime \prime }+3 t \left (1+3 t \right ) y^{\prime }+\left (-t^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| 12248 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{2 x}+3 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| 12249 |
\begin{align*}
x^{\prime }&=2 x-3 y+2 \sin \left (2 t \right ) \\
y^{\prime }&=x-2 y-\cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| 12250 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| 12251 |
\begin{align*}
3 x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| 12252 |
\begin{align*}
x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| 12253 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=x^{3} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.028 |
|
| 12254 |
\begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.028 |
|
| 12255 |
\begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.028 |
|
| 12256 |
\begin{align*}
y&=x y^{\prime }+\frac {m}{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.028 |
|
| 12257 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.028 |
|
| 12258 |
\begin{align*}
t y^{\prime \prime }+3 y&=t \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.029 |
|
| 12259 |
\begin{align*}
t^{4} x^{\prime \prime \prime \prime }-2 t^{3} x^{\prime \prime \prime }-20 t^{2} x^{\prime \prime }+12 x^{\prime } t +16 x&=\cos \left (3 \ln \left (t \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.029 |
|
| 12260 |
\begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+a x&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
1.029 |
|
| 12261 |
\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*} |
✓ |
✓ |
✓ |
✗ |
1.029 |
|
| 12262 |
\begin{align*}
2 y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| 12263 |
\begin{align*}
y^{\prime }&=y^{2} \left (4-y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| 12264 |
\begin{align*}
{y^{\prime }}^{2} x -y y^{\prime }-2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.030 |
|
| 12265 |
\begin{align*}
y+y^{\prime }&=\delta \left (t -5\right ) \\
y \left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| 12266 |
\begin{align*}
\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }&=c y^{2}-b \,x^{m -1} y+a \,x^{-2+n} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
1.030 |
|
| 12267 |
\begin{align*}
x_{1}^{\prime }&=-4 x_{1}+2 x_{2}-x_{3} \\
x_{2}^{\prime }&=-6 x_{1}-3 x_{3} \\
x_{3}^{\prime }&=\frac {8 x_{2}}{3}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| 12268 |
\begin{align*}
y^{\prime }&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| 12269 |
\begin{align*}
y^{\prime \prime } y^{\prime \prime \prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.030 |
|
| 12270 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }-\left (x^{2}+1\right ) y&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.030 |
|
| 12271 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+\left (x +4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| 12272 |
\begin{align*}
y^{2} y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.030 |
|
| 12273 |
\begin{align*}
x^{\prime }+5 x-2 y&=0 \\
2 x+y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.031 |
|
| 12274 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {n \left (n +1\right ) y}{x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.031 |
|
| 12275 |
\(\left [\begin {array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 4 & 1 & 0 \\ 0 & 0 & -3 & 1 \\ 0 & 0 & 1 & -2 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
1.031 |
|
| 12276 |
\begin{align*}
2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| 12277 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| 12278 |
\begin{align*}
\left (x +y^{2}\right ) y^{\prime \prime }-2 \left (x -y^{2}\right ) {y^{\prime }}^{3}+y^{\prime } \left (1+4 y y^{\prime }\right )&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
1.032 |
|
| 12279 |
\begin{align*}
x^{\prime \prime }+x&=\frac {1}{t +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| 12280 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+5 y&=2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| 12281 |
\begin{align*}
x^{\prime }&=3 x+a y \\
y^{\prime }&=-6 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| 12282 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} t +4 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| 12283 |
\begin{align*}
x^{\prime }-x+2 y^{\prime }+7 y&=3 t -15 \\
2 x^{\prime }+y^{\prime }+x+5 y&=9 t -7 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| 12284 |
\begin{align*}
2 y^{\prime \prime }-3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12285 |
\begin{align*}
4 x^{2} y^{\prime \prime }+x \left (4 x^{2}+2 x +7\right ) y^{\prime }-\left (-7 x^{2}-4 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12286 |
\begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12287 |
\begin{align*}
\left (y+1\right ) y^{\prime \prime }&=3 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.033 |
|
| 12288 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=8 x^{2} {\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12289 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.033 |
|
| 12290 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}-v \left (v -1\right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12291 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\sinh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.033 |
|
| 12292 |
\begin{align*}
y^{\prime \prime }-4 y&={\mathrm e}^{2 x} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12293 |
\begin{align*}
{y^{\prime }}^{2}-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12294 |
\begin{align*}
y^{\prime \prime }+y&=x \,{\mathrm e}^{x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12295 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12296 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=4 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 12297 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=\cos \left (x \right )-{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.034 |
|
| 12298 |
\begin{align*}
x^{\prime }&=-3 x-5 y \\
y^{\prime }&=3 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.034 |
|
| 12299 |
\begin{align*}
x^{\prime }&=\left (a -2\right ) x+y \\
y^{\prime }&=-x+\left (a -2\right ) y \\
z^{\prime }&=-a z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.034 |
|
| 12300 |
\begin{align*}
x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.034 |
|