| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 16401 |
\begin{align*}
y^{\prime \prime }+p \left (x \right ) y^{\prime }+q \left (x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.325 |
|
| 16402 |
\begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.325 |
|
| 16403 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-a -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.326 |
|
| 16404 |
\begin{align*}
\left (-x +a \right )^{2} \left (-x +b \right )^{2} y^{\prime \prime }&=k^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.326 |
|
| 16405 |
\begin{align*}
y^{\prime }-4 y&=32 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.326 |
|
| 16406 |
\begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}+b x y+c \,x^{2 n}+s \,x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.326 |
|
| 16407 |
\begin{align*}
y^{\prime \prime }&={\mathrm e}^{y} y^{\prime } \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.326 |
|
| 16408 |
\begin{align*}
y^{\prime \prime } \left (1+2 \ln \left (y^{\prime }\right )\right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.326 |
|
| 16409 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.327 |
|
| 16410 |
\begin{align*}
y^{\prime }-y x&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.327 |
|
| 16411 |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.327 |
|
| 16412 |
\begin{align*}
y^{\prime }+\frac {1}{2 y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.328 |
|
| 16413 |
\begin{align*}
5 x^{\prime }+x&=\sin \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.328 |
|
| 16414 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.329 |
|
| 16415 |
\begin{align*}
y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.329 |
|
| 16416 |
\begin{align*}
x^{\prime \prime }+4 x^{3}&=0 \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.330 |
|
| 16417 |
\begin{align*}
x y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.331 |
|
| 16418 |
\begin{align*}
x^{\prime \prime }+9 x&=0 \\
x \left (0\right ) &= {\frac {1}{3}} \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.331 |
|
| 16419 |
\begin{align*}
2 y^{\prime }-\frac {x}{y}&=\frac {x y}{x^{2}-1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.331 |
|
| 16420 |
\begin{align*}
{y^{\prime }}^{3}+x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.332 |
|
| 16421 |
\begin{align*}
y^{\prime \prime }&=-\frac {27 x y}{16 \left (x^{3}-1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.332 |
|
| 16422 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.333 |
|
| 16423 |
\begin{align*}
x \left (x +1\right ) y^{\prime }+y x&=1 \\
y \left ({\mathrm e}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.333 |
|
| 16424 |
\begin{align*}
y^{\prime \prime }&=x {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.333 |
|
| 16425 |
\begin{align*}
x^{\prime }&=c y-b z \\
y^{\prime }&=a z-c x \\
z^{\prime }&=b x-a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.334 |
|
| 16426 |
\begin{align*}
x^{\prime }+a x&=b t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.334 |
|
| 16427 |
\begin{align*}
2 x y^{2}+3 x^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.335 |
|
| 16428 |
\begin{align*}
n \,x^{3} y^{\prime \prime }&=\left (-x y^{\prime }+y\right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.335 |
|
| 16429 |
\begin{align*}
x^{2} y^{\prime \prime }-9 x y^{\prime }+24 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.335 |
|
| 16430 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=\sin \left (2 x \right ) \\
y \left (\frac {\pi }{4}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.336 |
|
| 16431 |
\begin{align*}
y^{\prime }&=\frac {y}{t^{2}}+4 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.336 |
|
| 16432 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+1&=3 \sin \left (2 x \right )+\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.336 |
|
| 16433 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.336 |
|
| 16434 |
\begin{align*}
-2 y+y^{\prime }&=4 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )\right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.337 |
|
| 16435 |
\begin{align*}
y^{\prime \prime }+18 \sin \left (y\right ) \cos \left (y\right )^{3}&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.337 |
|
| 16436 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.338 |
|
| 16437 |
\begin{align*}
y+\left (-x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.339 |
|
| 16438 |
\begin{align*}
\sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
2.339 |
|
| 16439 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&=13 \operatorname {Heaviside}\left (-4+t \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.339 |
|
| 16440 |
\begin{align*}
t y^{\prime }+y&=\cos \left (t \right ) t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.339 |
|
| 16441 |
\begin{align*}
x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.340 |
|
| 16442 |
\begin{align*}
-a y-3 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.342 |
|
| 16443 |
\begin{align*}
x y^{\prime \prime }&={y^{\prime }}^{3}+y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| 16444 |
\begin{align*}
t x^{\prime \prime }+x^{\prime }&=1 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| 16445 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+4 {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| 16446 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.343 |
|
| 16447 |
\begin{align*}
3 x -6&=x y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.345 |
|
| 16448 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.345 |
|
| 16449 |
\begin{align*}
x y^{\prime }+3 y&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.346 |
|
| 16450 |
\begin{align*}
y^{\prime }&=t -y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.346 |
|
| 16451 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.347 |
|
| 16452 |
\begin{align*}
x y^{\prime }+y&=x^{4} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.347 |
|
| 16453 |
\begin{align*}
y^{\prime }-k y&=A \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.347 |
|
| 16454 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.348 |
|
| 16455 |
\begin{align*}
y^{\prime }&=\frac {2 y}{-t^{2}+1}+3 \\
y \left (\frac {1}{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.349 |
|
| 16456 |
\begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=x^{m +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.349 |
|
| 16457 |
\begin{align*}
x y^{\prime }-x \sqrt {x^{2}+y^{2}}-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.349 |
|
| 16458 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
y \left (-1\right ) &= 0 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.349 |
|
| 16459 |
\begin{align*}
y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.350 |
|
| 16460 |
\begin{align*}
y^{\prime \prime }-a x y^{\prime }-b x y-x^{3} c&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.350 |
|
| 16461 |
\begin{align*}
4 y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.350 |
|
| 16462 |
\begin{align*}
2 y+t y^{\prime }&=\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.351 |
|
| 16463 |
\begin{align*}
y^{\prime }+y&=\frac {{\mathrm e}^{x}}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.351 |
|
| 16464 |
\begin{align*}
y^{\prime }-y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.351 |
|
| 16465 |
\begin{align*}
y^{\prime }-2 y x&={\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.352 |
|
| 16466 |
\begin{align*}
y^{\prime }+y&={\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.352 |
|
| 16467 |
\begin{align*}
-y+y^{\prime }&=4 t \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.352 |
|
| 16468 |
\begin{align*}
1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.352 |
|
| 16469 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.352 |
|
| 16470 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.353 |
|
| 16471 |
\begin{align*}
y+\ln \left (t \right ) y^{\prime }&=\cot \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.355 |
|
| 16472 |
\begin{align*}
y^{\prime }&=y^{2} {\mathrm e}^{-x}+y-{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.356 |
|
| 16473 |
\begin{align*}
{y^{\prime \prime \prime }}^{2}&={y^{\prime \prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.356 |
|
| 16474 |
\begin{align*}
y^{\prime }-2 y&=\cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.357 |
|
| 16475 |
\begin{align*}
y^{\prime }&=y^{2}-y^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.357 |
|
| 16476 |
\begin{align*}
y^{\prime }&=f \left (x \right ) g \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.358 |
|
| 16477 |
\begin{align*}
y^{\prime }&=1+3 y \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.358 |
|
| 16478 |
\begin{align*}
y^{\prime \prime }+k^{2} y&=k \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.358 |
|
| 16479 |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y^{2}-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.359 |
|
| 16480 |
\begin{align*}
t^{2} y^{\prime \prime }-12 t y^{\prime }+42 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.359 |
|
| 16481 |
\begin{align*}
y^{\prime }+2 y^{\prime \prime \prime }+y^{\left (5\right )}&=a x +\cos \left (x \right ) b +c \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.360 |
|
| 16482 |
\begin{align*}
x y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.360 |
|
| 16483 |
\begin{align*}
y^{\prime \prime }+\left (1+\frac {1}{x^{2}+1}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
2.360 |
|
| 16484 |
\begin{align*}
{y^{\prime \prime }}^{3}&=12 y^{\prime } \left (-2 y^{\prime }+x y^{\prime \prime }\right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.361 |
|
| 16485 |
\begin{align*}
x^{3} y^{\prime }-x^{6} y^{2}-\left (2 x -3\right ) x^{2} y+3&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.361 |
|
| 16486 |
\begin{align*}
2 x^{2} y y^{\prime \prime }+4 y^{2}&={y^{\prime }}^{2} x^{2}+2 x y y^{\prime } \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.361 |
|
| 16487 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=2 x \left (x -y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.362 |
|
| 16488 |
\begin{align*}
i^{\prime }-6 i&=10 \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.362 |
|
| 16489 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.362 |
|
| 16490 |
\begin{align*}
y^{\prime }&=\sin \left (y\right )-\cos \left (x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.362 |
|
| 16491 |
\begin{align*}
-3 y+\left (2-x \right ) y^{\prime }+\left (2-x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.363 |
|
| 16492 |
\begin{align*}
L i^{\prime }+R i&=E \\
i \left (0\right ) &= i_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.363 |
|
| 16493 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.363 |
|
| 16494 |
\begin{align*}
y^{\prime }&=\frac {x}{2}-y+\frac {3}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.363 |
|
| 16495 |
\begin{align*}
y^{\prime \prime }+2 y+t \sin \left (y\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.363 |
|
| 16496 |
\begin{align*}
y^{\prime }&=-y+\operatorname {Heaviside}\left (-3+t \right )+\delta \left (t -1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.363 |
|
| 16497 |
\begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.364 |
|
| 16498 |
\begin{align*}
y^{\prime }&=2 t \cos \left (y\right )^{2} \\
y \left (0\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.364 |
|
| 16499 |
\begin{align*}
{y^{\prime }}^{3}-f \left (x \right ) \left (a y^{2}+b y+c \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.364 |
|
| 16500 |
\begin{align*}
x^{\prime }&=7 x \left (x-13\right ) \\
x \left (0\right ) &= 17 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.365 |
|