| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15301 |
\begin{align*}
y^{\prime \prime }+y&=2 \cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.259 |
|
| 15302 |
\begin{align*}
2 x^{2} y^{\prime \prime }+2 y^{\prime } x -y x&=x^{3}+x \sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.260 |
|
| 15303 |
\begin{align*}
\left (-1+x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.260 |
|
| 15304 |
\begin{align*}
\left (8 {y^{\prime }}^{3}-27\right ) x&=12 y {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.260 |
|
| 15305 |
\begin{align*}
\frac {y}{t}+y^{\prime }&=3 \cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.262 |
|
| 15306 |
\begin{align*}
b y+a y^{\prime }+y^{\prime \prime }&=f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.263 |
|
| 15307 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.264 |
|
| 15308 |
\begin{align*}
\left (x +1\right ) y^{\prime }&={\mathrm e}^{x} \left (x +1\right )^{n +1}+n y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.265 |
|
| 15309 |
\begin{align*}
y^{\prime }+4 y&=t \,{\mathrm e}^{-4 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.265 |
|
| 15310 |
\begin{align*}
x {y^{\prime }}^{2}-2 y y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.266 |
|
| 15311 |
\begin{align*}
x {y^{\prime }}^{2}-2 y y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.266 |
|
| 15312 |
\begin{align*}
x^{\prime }&=3 x-\frac {y}{2}-3 t^{2}-\frac {t}{2}+\frac {3}{2} \\
y^{\prime }&=2 y-2 t -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.268 |
|
| 15313 |
\begin{align*}
y^{\prime \prime }-2 \alpha y^{\prime }+\left (\alpha ^{2}-\epsilon ^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.269 |
|
| 15314 |
\begin{align*}
-a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.270 |
|
| 15315 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=2 x^{2} {\mathrm e}^{-2 x}+3 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.270 |
|
| 15316 |
\(\left [\begin {array}{ccc} 5 & 0 & 2 \\ 0 & 0 & 0 \\ 2 & 0 & 0 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
3.270 |
|
| 15317 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-10 x_{2} \\
x_{2}^{\prime }&=-x_{1}-x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -3 \\
x_{2} \left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.270 |
|
| 15318 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.272 |
|
| 15319 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=5 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.273 |
|
| 15320 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-p^{2}+x^{2}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.273 |
|
| 15321 |
\begin{align*}
y y^{\prime }&=x \left (1+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.274 |
|
| 15322 |
\begin{align*}
\cos \left (y\right ) \sin \left (x \right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.274 |
|
| 15323 |
\begin{align*}
y^{\prime } x +a y^{2}-b y+c \,x^{2 b}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.275 |
|
| 15324 |
\begin{align*}
x^{2} y^{\prime }-\left (-1+x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.275 |
|
| 15325 |
\begin{align*}
y y^{\prime }&=-1+x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.276 |
|
| 15326 |
\begin{align*}
y^{\prime }+2 y \left (1-x \sqrt {y}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.276 |
|
| 15327 |
\begin{align*}
m y^{\prime \prime }+b y^{\prime }+k y&=\cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.276 |
|
| 15328 |
\begin{align*}
x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x&=F \cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.276 |
|
| 15329 |
\begin{align*}
t y+\left (t^{2}+1\right ) y^{\prime }&=\left (t^{2}+1\right )^{{5}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.277 |
|
| 15330 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.277 |
|
| 15331 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.278 |
|
| 15332 |
\begin{align*}
y^{\prime }-\frac {2 x y}{x^{2}+1}&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.279 |
|
| 15333 |
\begin{align*}
x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.280 |
|
| 15334 |
\begin{align*}
a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.280 |
|
| 15335 |
\begin{align*}
y^{\prime }&=2 x \left (\pi +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.281 |
|
| 15336 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.283 |
|
| 15337 |
\begin{align*}
3 y-2 x +\left (3 x -2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.284 |
|
| 15338 |
\begin{align*}
y^{\prime \prime } x +\left (2 x +3\right ) y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.284 |
|
| 15339 |
\begin{align*}
3 \sin \left (x \right )-4 y^{\prime } \cos \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.284 |
|
| 15340 |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=a \,x^{3}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.285 |
|
| 15341 |
\begin{align*}
\tan \left (x \right ) y^{\prime }+y&=\cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.286 |
|
| 15342 |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.286 |
|
| 15343 |
\begin{align*}
x^{2} \left (-x^{2}+1\right ) y^{\prime }&=\left (x -3 x^{3} y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.286 |
|
| 15344 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=8 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.286 |
|
| 15345 |
\begin{align*}
2 \left (x +3\right )^{2} y^{\prime \prime }-\left (x^{2}+5 x +6\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=-3\). |
✓ |
✓ |
✓ |
✓ |
3.286 |
|
| 15346 |
\begin{align*}
y \left (y-2 y^{\prime } x \right )^{3}&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.287 |
|
| 15347 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.288 |
|
| 15348 |
\begin{align*}
x^{\prime }-k^{2} x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.288 |
|
| 15349 |
\begin{align*}
y^{\prime }&=y \sqrt {t} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.290 |
|
| 15350 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.292 |
|
| 15351 |
\begin{align*}
y^{\prime \prime }+16 y&=8 x +8 \sin \left (4 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.292 |
|
| 15352 |
\begin{align*}
2+y^{2}+2 x +2 y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.293 |
|
| 15353 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.293 |
|
| 15354 |
\begin{align*}
y^{\prime }-x y^{2}-3 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.293 |
|
| 15355 |
\begin{align*}
y^{\prime }-a \,x^{n} \left (1+y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.293 |
|
| 15356 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=\cosh \left (2 x \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
3.293 |
|
| 15357 |
\begin{align*}
y^{\prime \prime } x -y^{\prime } x +y&=x^{3} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.294 |
|
| 15358 |
\begin{align*}
1+{y^{\prime }}^{2}&=\frac {1}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.295 |
|
| 15359 |
\begin{align*}
y^{\prime \prime } x +\left (3 x +4\right ) y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.296 |
|
| 15360 |
\begin{align*}
x -\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.296 |
|
| 15361 |
\begin{align*}
4 y+y^{\prime \prime }&=\cos \left (x \right ) \cos \left (2 x \right ) \cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.297 |
|
| 15362 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}+1 \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+3 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.297 |
|
| 15363 |
\begin{align*}
y^{\prime }&=1-t +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.299 |
|
| 15364 |
\begin{align*}
y^{\prime }&=r \left (a -y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.299 |
|
| 15365 |
\begin{align*}
y^{\prime } x +y&=x^{4} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.299 |
|
| 15366 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=x_{1}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.299 |
|
| 15367 |
\begin{align*}
y^{\prime }-y&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.300 |
|
| 15368 |
\begin{align*}
y^{\prime }&=3-6 x +y-2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.301 |
|
| 15369 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.302 |
|
| 15370 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (x \right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.303 |
|
| 15371 |
\begin{align*}
m s^{\prime \prime }&=\frac {g \,t^{2}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.303 |
|
| 15372 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) \left (y \sec \left (x \right )-2\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.304 |
|
| 15373 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left ({\mathrm e}^{\frac {2}{x}}-v^{2}\right ) y}{x^{4}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.304 |
|
| 15374 |
\begin{align*}
2 \left (1-x \right ) x \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime }&=f \left (x \right ) \left (\left (1-y\right ) \left (x -y\right ) y\right )^{{3}/{2}}-y^{2} \left (1-y^{2}\right )+2 \left (1-y\right ) y \left (x^{2}+y-2 y x \right ) y^{\prime }+\left (1-x \right ) x \left (x -2 y-2 y x +3 y^{2}\right ) {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3.305 |
|
| 15375 |
\begin{align*}
25 x^{2} y^{\prime \prime }+\left (4+2 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.305 |
|
| 15376 |
\begin{align*}
y^{\prime \prime } x +\left (x^{3}-1\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.306 |
|
| 15377 |
\begin{align*}
x \left (x -2\right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (-1+x \right ) y&=3 x^{2} \left (x -2\right )^{2} {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.306 |
|
| 15378 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime } x -{\mathrm e}^{x} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.306 |
|
| 15379 |
\begin{align*}
\left (t^{2}+4\right ) y^{\prime }+2 t y&=2 t \\
y \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.306 |
|
| 15380 |
\begin{align*}
\cot \left (x \right ) y^{\prime }+y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.307 |
|
| 15381 |
\begin{align*}
y&=y^{\prime } x -\sqrt {y^{\prime }-1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.307 |
|
| 15382 |
\begin{align*}
y^{\left (5\right )}+4 y^{\prime \prime \prime }&={\mathrm e}^{x}+3 \sin \left (2 x \right )+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.307 |
|
| 15383 |
\begin{align*}
y^{\prime }&={\mathrm e}^{a x}+a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.309 |
|
| 15384 |
\(\left [\begin {array}{ccc} -1 & 0 & 3-i \\ 0 & 1 & 0 \\ 3+i & 0 & 0 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
3.309 |
|
| 15385 |
\begin{align*}
y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.310 |
|
| 15386 |
\begin{align*}
y^{\prime }-\frac {y-x f \left (x^{2}+a y^{2}\right )}{x +a y f \left (x^{2}+a y^{2}\right )}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.310 |
|
| 15387 |
\begin{align*}
y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y&=-t^{2}+2 t -10 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
3.310 |
|
| 15388 |
\begin{align*}
x&=y \left (y^{\prime }+\frac {1}{y^{\prime }}\right )+{y^{\prime }}^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.312 |
|
| 15389 |
\begin{align*}
\left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.313 |
|
| 15390 |
\begin{align*}
y^{\prime \prime }&=6 \sin \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.314 |
|
| 15391 |
\begin{align*}
4 {y^{\prime }}^{2}-2 \left (y+3 y^{\prime } x \right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.315 |
|
| 15392 |
\begin{align*}
y^{\prime }+i y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.316 |
|
| 15393 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.316 |
|
| 15394 |
\begin{align*}
y^{\prime \prime } x +\left (x -6\right ) y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.317 |
|
| 15395 |
\begin{align*}
y^{\prime \prime }+\left (a \cos \left (x \right )^{2}+b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.317 |
|
| 15396 |
\begin{align*}
y^{\prime \prime }+16 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.317 |
|
| 15397 |
\begin{align*}
x^{\prime }&=-\lambda x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.319 |
|
| 15398 |
\begin{align*}
y^{\prime }&=2 x -\left (x^{2}+1\right ) y+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.320 |
|
| 15399 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.320 |
|
| 15400 |
\begin{align*}
y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.322 |
|