| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 24401 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\sin \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.303 |
|
| 24402 |
\begin{align*}
\left (2 x +3 y+2\right ) y^{\prime }&=1-2 x -3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.309 |
|
| 24403 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+2 y&=x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.316 |
|
| 24404 |
\begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.318 |
|
| 24405 |
\begin{align*}
y^{\prime } \left (1+\sinh \left (x \right )\right ) \sinh \left (y\right )+\cosh \left (x \right ) \left (\cosh \left (y\right )-1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.325 |
|
| 24406 |
\begin{align*}
x y^{\prime }-y&=x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.326 |
|
| 24407 |
\begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.327 |
|
| 24408 |
\begin{align*}
x y^{\prime }+y&=\frac {1}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.336 |
|
| 24409 |
\begin{align*}
2 \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=y^{3} \sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.341 |
|
| 24410 |
\begin{align*}
y^{\prime }&=y^{2}+a x \sinh \left (b x \right )^{m} y+a \sinh \left (b x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.343 |
|
| 24411 |
\begin{align*}
x y^{\prime }&=y-x \cot \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.345 |
|
| 24412 |
\begin{align*}
x y^{\prime }&=y-x \left (x -y\right ) \sqrt {x^{2}+y^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
13.348 |
|
| 24413 |
\begin{align*}
x^{\prime }&=2 t x^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.350 |
|
| 24414 |
\begin{align*}
\left (x +y\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.358 |
|
| 24415 |
\begin{align*}
3 y+\left (7 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.363 |
|
| 24416 |
\begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.366 |
|
| 24417 |
\begin{align*}
x -y-3+\left (3 x -3 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.401 |
|
| 24418 |
\begin{align*}
4 x y y^{\prime }&=1+y^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.404 |
|
| 24419 |
\begin{align*}
\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right )&=1+\sin \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.405 |
|
| 24420 |
\begin{align*}
{y^{\prime }}^{3}&=a \,x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.408 |
|
| 24421 |
\begin{align*}
y^{\prime }&=\alpha y^{2}+\beta +\gamma \cosh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.408 |
|
| 24422 |
\begin{align*}
x y^{\prime }-y&=x \cot \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.414 |
|
| 24423 |
\begin{align*}
y^{\prime }&=x^{m -1} y^{1-n} f \left (a \,x^{m}+b y^{n}\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
13.417 |
|
| 24424 |
\begin{align*}
y^{\prime }+1&=2 \left (-x +y\right ) \left (y^{\prime }-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.418 |
|
| 24425 |
\begin{align*}
y&=x y^{\prime }-x^{2} {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
13.421 |
|
| 24426 |
\begin{align*}
y+y^{2} x^{4}+x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.424 |
|
| 24427 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+13 x&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 1-t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.428 |
|
| 24428 |
\begin{align*}
2 x \left (2 x +y\right ) y^{\prime }&=y \left (4 x -y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.434 |
|
| 24429 |
\begin{align*}
\left (\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
13.437 |
|
| 24430 |
\begin{align*}
{y^{\prime \prime }}^{2}&={y^{\prime }}^{2} \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.437 |
|
| 24431 |
\begin{align*}
6 x -3 y+2-\left (2 x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.438 |
|
| 24432 |
\begin{align*}
x^{2} y^{\prime \prime }-y&=\sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.443 |
|
| 24433 |
\begin{align*}
x y^{\prime }+y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.448 |
|
| 24434 |
\begin{align*}
\left (1-4 x -2 y\right ) y^{\prime }+2 x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.451 |
|
| 24435 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.456 |
|
| 24436 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}-a \,x^{n} \left (b \,{\mathrm e}^{\lambda x}+c \right ) y+c \,x^{n} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
13.459 |
|
| 24437 |
\begin{align*}
y^{\prime }&=\sqrt {{| y|}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.466 |
|
| 24438 |
\begin{align*}
y^{\prime }&=x^{3} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.472 |
|
| 24439 |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.478 |
|
| 24440 |
\begin{align*}
y^{\prime }&=\lambda \sin \left (\lambda x \right ) y^{2}+a \,x^{n} \cos \left (\lambda x \right ) y-a \,x^{n} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
13.485 |
|
| 24441 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (x -1\right )}-\frac {\left (a x +b \right ) y}{4 x \left (x -1\right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
13.493 |
|
| 24442 |
\begin{align*}
y^{\prime }&=-F \left (x \right ) \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{x \ln \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.498 |
|
| 24443 |
\begin{align*}
\left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.502 |
|
| 24444 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=\ln \left (x \right )^{2}-\ln \left (x^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.503 |
|
| 24445 |
\begin{align*}
\left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.504 |
|
| 24446 |
\begin{align*}
y^{\prime \prime }+\sin \left (y\right )&=0 \\
y \left (\infty \right ) &= \pi \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
13.510 |
|
| 24447 |
\begin{align*}
x^{\prime \prime }+x-x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.512 |
|
| 24448 |
\begin{align*}
y y^{\prime }+y^{4}&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
13.519 |
|
| 24449 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.521 |
|
| 24450 |
\begin{align*}
x^{3}-x y^{2}+y+\left (y^{3}-x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.523 |
|
| 24451 |
\begin{align*}
x^{\prime }&=-t^{2} x^{2} \\
x \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.530 |
|
| 24452 |
\begin{align*}
y&=2 x y^{\prime }+\ln \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.536 |
|
| 24453 |
\begin{align*}
x y^{\prime }-y&=\left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.540 |
|
| 24454 |
\begin{align*}
1+{y^{\prime }}^{2}+2 y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.541 |
|
| 24455 |
\begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.543 |
|
| 24456 |
\begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.547 |
|
| 24457 |
\begin{align*}
x y^{\prime }&=y \ln \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.551 |
|
| 24458 |
\begin{align*}
x^{3} y+\left (3 x^{4}-y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.551 |
|
| 24459 |
\begin{align*}
2 y y^{\prime \prime }&=a +{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.553 |
|
| 24460 |
\begin{align*}
y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.553 |
|
| 24461 |
\begin{align*}
y y^{\prime }+x&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.566 |
|
| 24462 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} f \left (x \right ) y^{\prime }+\left (x^{2} \left (f^{\prime }\left (x \right )+f \left (x \right )^{2}+a \right )-v \left (v -1\right )\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
13.567 |
|
| 24463 |
\begin{align*}
\frac {y+\sin \left (x \right ) \cos \left (y x \right )^{2}}{\cos \left (y x \right )^{2}}+\left (\frac {x}{\cos \left (y x \right )^{2}}+\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
13.574 |
|
| 24464 |
\begin{align*}
{y^{\prime }}^{3}+y^{\prime }&={\mathrm e}^{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.579 |
|
| 24465 |
\begin{align*}
x y^{\prime }&=x \sqrt {y-x^{2}}+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.579 |
|
| 24466 |
\begin{align*}
\left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.582 |
|
| 24467 |
\begin{align*}
2 x^{2} y^{2}+y+\left (x^{3} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.585 |
|
| 24468 |
\begin{align*}
x^{2} \left (a \,x^{n}-1\right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (p \,x^{n}+q \right ) x y+r \,x^{n}+s&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.587 |
|
| 24469 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.603 |
|
| 24470 |
\begin{align*}
x y^{\prime }+y&=2 x \\
y \left (x_{0} \right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.616 |
|
| 24471 |
\begin{align*}
y^{\prime }&=a y-b y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.635 |
|
| 24472 |
\begin{align*}
4 {y^{\prime }}^{2}-2 \left (3 x y^{\prime }+y\right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
13.648 |
|
| 24473 |
\begin{align*}
x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.648 |
|
| 24474 |
\begin{align*}
y^{\prime }&=\frac {\left (3+2 y\right )^{2}}{\left (5+4 x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.648 |
|
| 24475 |
\begin{align*}
y^{2}+y x +1+\left (x^{2}+y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.652 |
|
| 24476 |
\begin{align*}
v \left (3 x +2 v\right )-x^{2} v^{\prime }&=0 \\
v \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.652 |
|
| 24477 |
\begin{align*}
y^{\prime }&=\frac {y}{x -y+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.653 |
|
| 24478 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (-3+t \right ) \\
y \left (0\right ) &= -{\frac {2}{3}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
13.658 |
|
| 24479 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.663 |
|
| 24480 |
\begin{align*}
y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.667 |
|
| 24481 |
\begin{align*}
y^{\prime }&=\lambda \sin \left (\lambda x \right ) y^{2}+a \sin \left (\lambda x \right ) y-a \tan \left (\lambda x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
13.669 |
|
| 24482 |
\begin{align*}
\left (a +b \sinh \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
13.670 |
|
| 24483 |
\begin{align*}
3 x -2 y+1+\left (3 x -2 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.679 |
|
| 24484 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda a +b \lambda +2 a b +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2}+b \left (\lambda -b \right ) \cot \left (\lambda x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
13.683 |
|
| 24485 |
\begin{align*}
y^{\prime }&=\alpha \left (A -y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.689 |
|
| 24486 |
\begin{align*}
y y^{\prime \prime }&=2 {y^{\prime }}^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= \sqrt {3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.691 |
|
| 24487 |
\begin{align*}
x +2 y-1-\left (x +2 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.698 |
|
| 24488 |
\begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}+2 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.701 |
|
| 24489 |
\begin{align*}
3 x -3 y-2-\left (x -y+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.702 |
|
| 24490 |
\begin{align*}
-a \left (a +1\right ) \csc \left (x \right )^{2} y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
13.704 |
|
| 24491 |
\begin{align*}
y y^{\prime }-y&=\frac {A}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.706 |
|
| 24492 |
\begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.710 |
|
| 24493 |
\begin{align*}
\left (p \left (1+p \right )-k^{2} \csc \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
13.729 |
|
| 24494 |
\begin{align*}
y^{\prime }&=t^{2} \tan \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.732 |
|
| 24495 |
\begin{align*}
y^{\prime }-\frac {1+y^{2}}{{| y+\sqrt {y+1}|} \left (x +1\right )^{{3}/{2}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.746 |
|
| 24496 |
\begin{align*}
y y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.756 |
|
| 24497 |
\begin{align*}
y^{\prime }&=\frac {\left (5-2 \cos \left (x \right )\right )^{3} \sin \left (x \right ) \cos \left (y\right )^{4}}{\sin \left (y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.776 |
|
| 24498 |
\begin{align*}
\left (x +2 y+1\right ) y^{\prime }+1-x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.781 |
|
| 24499 |
\begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
13.782 |
|
| 24500 |
\begin{align*}
y+\left (x -2 x^{2} y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
13.792 |
|