| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 13401 |
\begin{align*}
{\mathrm e}^{x}-y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.457 |
|
| 13402 |
\begin{align*}
\left (y^{3}+1\right ) y^{\prime }&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.457 |
|
| 13403 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=\frac {1}{x^{2}+1} \\
y \left (\infty \right ) &= \frac {\pi ^{2}}{8} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
2.458 |
|
| 13404 |
\begin{align*}
1-\sin \left (x \right ) y-\cos \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.459 |
|
| 13405 |
\begin{align*}
2 \left (-x^{k}+4 x^{3}\right ) \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )-\left (-12 x^{2}+k \,x^{-1+k}\right ) \left (y^{2}+3 y^{\prime }\right )+a x y+b&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.459 |
|
| 13406 |
\begin{align*}
x y^{2}-6+x^{2} y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.459 |
|
| 13407 |
\begin{align*}
y+y^{2} x^{4}+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.459 |
|
| 13408 |
\begin{align*}
y^{\prime } x +\left (b x +a \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.460 |
|
| 13409 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x -x^{2}-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.460 |
|
| 13410 |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+b x \left (-b \,x^{3}+a x +2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.460 |
|
| 13411 |
\begin{align*}
\frac {y}{4}+y^{\prime }&=3+2 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.460 |
|
| 13412 |
\begin{align*}
y y^{\prime }+x \,{\mathrm e}^{x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.461 |
|
| 13413 |
\begin{align*}
y^{\prime }&=\frac {x \left (-x^{2}+2 x^{2} y-2 x^{4}+1\right )}{-x^{2}+y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.461 |
|
| 13414 |
\begin{align*}
y^{\prime }&={\mathrm e}^{t} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.461 |
|
| 13415 |
\begin{align*}
y^{\prime }&=x \left (x^{2}-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.462 |
|
| 13416 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=\left (1-x y^{3}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.463 |
|
| 13417 |
\begin{align*}
{y^{\prime }}^{2}&=\frac {1}{x^{2} y^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.463 |
|
| 13418 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y&=\frac {1}{x -2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.463 |
|
| 13419 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & 10\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.463 |
|
| 13420 |
\begin{align*}
y^{\prime \prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.463 |
|
| 13421 |
\begin{align*}
-a \,x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.465 |
|
| 13422 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.466 |
|
| 13423 |
\begin{align*}
y+y^{\prime }&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.466 |
|
| 13424 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.467 |
|
| 13425 |
\begin{align*}
x^{2}+2 x +y+\left (3 x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.467 |
|
| 13426 |
\begin{align*}
2 y a^{2} b^{2}+2 \left (a^{2}+b^{2}\right ) y^{\prime \prime }+2 y^{\prime \prime \prime \prime }&=\cos \left (a x \right )+\cos \left (b x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.468 |
|
| 13427 |
\begin{align*}
y^{\prime }&=\frac {2 y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.468 |
|
| 13428 |
\begin{align*}
4 y {y^{\prime }}^{2} y^{\prime \prime }&=3+{y^{\prime }}^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.468 |
|
| 13429 |
\begin{align*}
y^{\prime }&=y-{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.468 |
|
| 13430 |
\begin{align*}
2 x y^{2}+3 x^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.470 |
|
| 13431 |
\begin{align*}
y^{\prime \prime }&=\frac {\cos \left (2 x \right ) y^{\prime }}{\sin \left (2 x \right )}-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.470 |
|
| 13432 |
\begin{align*}
x^{\prime }&={\mathrm e}^{x}-t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.470 |
|
| 13433 |
\begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}&=b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.471 |
|
| 13434 |
\begin{align*}
\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.472 |
|
| 13435 |
\begin{align*}
y^{\prime }&=\cos \left (x \right ) \sin \left (x \right )+\cos \left (x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.472 |
|
| 13436 |
\begin{align*}
y^{\prime }+a y-b \sin \left (c x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.472 |
|
| 13437 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y-\sec \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.473 |
|
| 13438 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.474 |
|
| 13439 |
\begin{align*}
y^{\prime }+\tan \left (x \right ) y&=y^{3} \sec \left (x \right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.474 |
|
| 13440 |
\begin{align*}
y&=y^{\prime } x \left (1+y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.475 |
|
| 13441 |
\begin{align*}
y^{\prime }+y \tanh \left (x \right )&=2 \sinh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.475 |
|
| 13442 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a^{2} x^{2}-6\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.475 |
|
| 13443 |
\begin{align*}
y^{\prime \prime }&=-\frac {3 y}{16 x^{2} \left (x -1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.475 |
|
| 13444 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.476 |
|
| 13445 |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime }+2 y&=\left (x^{2}+1\right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.476 |
|
| 13446 |
\begin{align*}
\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime }&=2 y x -{\mathrm e}^{y}-x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.479 |
|
| 13447 |
\begin{align*}
y y^{\prime }&=x y^{2}+x \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.479 |
|
| 13448 |
\begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.480 |
|
| 13449 |
\begin{align*}
x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t}&=2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.480 |
|
| 13450 |
\begin{align*}
x^{\prime }&=k x \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.481 |
|
| 13451 |
\begin{align*}
x^{\prime \prime }&=x-x^{3} \\
x \left (0\right ) &= \frac {\sqrt {2}}{2} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.481 |
|
| 13452 |
\begin{align*}
\frac {y^{\prime }}{x^{2}+1}&=\frac {x}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.482 |
|
| 13453 |
\begin{align*}
y^{\prime }&=\frac {2 x y^{2}+x}{x^{2} y-y} \\
y \left (\sqrt {2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.483 |
|
| 13454 |
\begin{align*}
\csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.483 |
|
| 13455 |
\begin{align*}
\frac {x y^{\prime \prime }}{1-x}+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.483 |
|
| 13456 |
\begin{align*}
u^{\prime \prime }+16 u&=0 \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.483 |
|
| 13457 |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.484 |
|
| 13458 |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.484 |
|
| 13459 |
\begin{align*}
y^{\prime } x&=y+x^{2}+9 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.484 |
|
| 13460 |
\begin{align*}
y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.484 |
|
| 13461 |
\begin{align*}
y^{\prime }+q \left (x \right ) y&=0 \\
y \left (\textit {x\_0} \right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.485 |
|
| 13462 |
\begin{align*}
y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.486 |
|
| 13463 |
\begin{align*}
y^{\prime }+\frac {y}{1-x}+x -x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.486 |
|
| 13464 |
\begin{align*}
y^{\prime }&=t y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.486 |
|
| 13465 |
\begin{align*}
y^{\prime \prime }+2 i y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.487 |
|
| 13466 |
\begin{align*}
{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.487 |
|
| 13467 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
y \left (0\right ) &= 10 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.487 |
|
| 13468 |
\begin{align*}
y \ln \left (y\right )+y^{\prime } x&=y x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.487 |
|
| 13469 |
\begin{align*}
x^{2} y^{\prime }&=a +b x +c \,x^{2}+y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.488 |
|
| 13470 |
\begin{align*}
y^{\prime }&=\frac {1}{x -3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.489 |
|
| 13471 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.490 |
|
| 13472 |
\begin{align*}
x^{2} y^{\prime }&=a +b x +c \,x^{2}-y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.490 |
|
| 13473 |
\begin{align*}
y^{\prime }&=y^{2} {\mathrm e}^{-t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.490 |
|
| 13474 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+6 x_{2}+2 x_{3}-2 x_{4} \\
x_{2}^{\prime }&=2 x_{1}-3 x_{2}-6 x_{3}+2 x_{4} \\
x_{3}^{\prime }&=-4 x_{1}+8 x_{2}+3 x_{3}-4 x_{4} \\
x_{4}^{\prime }&=2 x_{1}-2 x_{2}-6 x_{3}+x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.490 |
|
| 13475 |
\begin{align*}
y^{\prime }+\frac {y}{\sin \left (x \right )}-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.490 |
|
| 13476 |
\begin{align*}
y y^{\prime }&=x y^{2}-9 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.491 |
|
| 13477 |
\begin{align*}
\left (-x^{2}+1\right ) {y^{\prime }}^{2}&=1-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.491 |
|
| 13478 |
\begin{align*}
y^{\prime }&=\frac {x}{y^{2} \sqrt {x +1}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.493 |
|
| 13479 |
\begin{align*}
y^{\prime \prime }+2 y&=-3 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.493 |
|
| 13480 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.493 |
|
| 13481 |
\begin{align*}
x \cos \left (y\right ) y^{\prime }-\left (x^{2}+1\right ) \sin \left (y\right )&=0 \\
y \left (1\right ) &= \frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.493 |
|
| 13482 |
\begin{align*}
\frac {x^{\prime \prime }}{32}+2 x^{\prime }+x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.494 |
|
| 13483 |
\begin{align*}
s^{\prime }&=\frac {1}{s+t +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.494 |
|
| 13484 |
\begin{align*}
2 y x -2 y+1+x \left (x -1\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.496 |
|
| 13485 |
\begin{align*}
y^{\prime }&=1-t +y^{2}-t y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.497 |
|
| 13486 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.497 |
|
| 13487 |
\begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.497 |
|
| 13488 |
\begin{align*}
2 x^{\prime }+y^{\prime }-x&=y+t \\
x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.498 |
|
| 13489 |
\begin{align*}
8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.498 |
|
| 13490 |
\begin{align*}
y^{\prime }&=-\frac {\left (\sqrt {a}\, x^{4}+\sqrt {a}\, x^{3}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
2.498 |
|
| 13491 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.499 |
|
| 13492 |
\begin{align*}
t^{2} y^{\prime \prime }+2 y^{\prime } t -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.499 |
|
| 13493 |
\begin{align*}
2 x +\frac {y}{1+y^{2} x^{2}}+\left (\frac {x}{1+y^{2} x^{2}}-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.500 |
|
| 13494 |
\begin{align*}
b \,{\mathrm e}^{2 a x} y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.500 |
|
| 13495 |
\begin{align*}
y \left (x -y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.500 |
|
| 13496 |
\begin{align*}
y^{\prime }+4 y&={\mathrm e}^{-2 t}+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.500 |
|
| 13497 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x +2 y^{2}&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.500 |
|
| 13498 |
\begin{align*}
y^{\prime \prime }-4 y&=12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.500 |
|
| 13499 |
\begin{align*}
y^{\prime \prime }&=y f^{\prime }\left (x \right )+\left (f \left (x \right )-2 y\right ) y^{\prime } \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.501 |
|
| 13500 |
\begin{align*}
y^{\prime }&=1+\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.502 |
|