| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 18501 |
\begin{align*}
{\mathrm e}^{y^{2}} \left (2 y^{\prime } y+\frac {2}{x}\right )&=\frac {1}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.311 |
|
| 18502 |
\begin{align*}
y+\left (-{\mathrm e}^{-2 y}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.311 |
|
| 18503 |
\begin{align*}
s^{\prime }+x^{2}&=x^{2} {\mathrm e}^{3 s} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.311 |
|
| 18504 |
\begin{align*}
y^{\prime } \cos \left (y\right )+\frac {\sin \left (y\right )}{x}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.312 |
|
| 18505 |
\begin{align*}
y^{\prime }&=x \sin \left (y\right )+{\mathrm e}^{x} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.312 |
|
| 18506 |
\begin{align*}
\left (2-10 x^{2} y^{3}+3 y^{2}\right ) y^{\prime }&=x \left (1+5 y^{4}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.313 |
|
| 18507 |
\begin{align*}
\left (y^{2}-x \right ) y^{\prime }-y+x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.313 |
|
| 18508 |
\begin{align*}
y^{\prime }+y x&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.315 |
|
| 18509 |
\begin{align*}
y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.316 |
|
| 18510 |
\begin{align*}
m v^{\prime }&=m g -k v^{2} \\
v \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.316 |
|
| 18511 |
\begin{align*}
\left (x -x^{2} y-y^{3}\right ) y^{\prime }&=x^{3}-y+x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.316 |
|
| 18512 |
\begin{align*}
3 y^{\prime \prime }-y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.316 |
|
| 18513 |
\begin{align*}
y^{\prime }&=\left (2 x^{2}-{\mathrm e}^{x} y\right ) {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.316 |
|
| 18514 |
\begin{align*}
y^{\prime } \left (y^{2}+2 x \right )&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.317 |
|
| 18515 |
\begin{align*}
y^{\prime }&=\frac {1+\sqrt {x}}{1+\sqrt {y}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.318 |
|
| 18516 |
\begin{align*}
y^{2}+1+\left (2 y x -y^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.318 |
|
| 18517 |
\begin{align*}
\left (x^{2}+y^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.318 |
|
| 18518 | \begin{align*}
s^{\prime }+s \cos \left (t \right )&=\frac {\sin \left (2 t \right )}{2} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.318 |
|
| 18519 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&=6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.318 |
|
| 18520 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.319 |
|
| 18521 |
\begin{align*}
4 x^{3} y^{2}-6 x^{2} y-2 x -3+\left (2 x^{4} y-2 x^{3}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.319 |
|
| 18522 |
\begin{align*}
x y^{\prime } y+x^{4}-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.319 |
|
| 18523 |
\begin{align*}
\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.319 |
|
| 18524 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{t} y}{1+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.319 |
|
| 18525 |
\begin{align*}
y^{\prime }+y x&=6 x \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.320 |
|
| 18526 |
\begin{align*}
y^{3}+4 \,{\mathrm e}^{x} y+\left (2 \,{\mathrm e}^{x}+3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.321 |
|
| 18527 |
\begin{align*}
y^{\prime }-2 y x&=4 x \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.321 |
|
| 18528 |
\begin{align*}
y^{\prime }&=\frac {y^{2}-4 t y+6 t^{2}}{t^{2}} \\
y \left (2\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.321 |
|
| 18529 |
\begin{align*}
\left (x -y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.323 |
|
| 18530 |
\begin{align*}
y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.325 |
|
| 18531 |
\begin{align*}
x \left (x^{3}-3 x^{3} y+4 y^{2}\right ) y^{\prime }&=6 y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.326 |
|
| 18532 |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{x +y}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.326 |
|
| 18533 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 4 \\
y \left (\pi \right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.327 |
|
| 18534 |
\begin{align*}
\left (x +1\right ) y^{\prime }+y&=\cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.328 |
|
| 18535 |
\begin{align*}
y^{\prime }&=\frac {2 \cos \left (2 x \right )}{3+2 y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.328 |
|
| 18536 |
\begin{align*}
\left (a \,x^{2}+b x +c \right )^{2} y^{\prime \prime }+\left (2 a x +k \right ) \left (a \,x^{2}+b x +c \right ) y^{\prime }+m y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.328 |
|
| 18537 | \begin{align*}
y^{\prime }+\left (\tan \left (x \right )+y^{2} \sec \left (x \right )\right ) y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.329 |
|
| 18538 |
\begin{align*}
y^{\prime }&=\sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.329 |
|
| 18539 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.329 |
|
| 18540 |
\begin{align*}
y^{\prime } y&=x y^{2}-9 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.329 |
|
| 18541 |
\begin{align*}
y^{\prime }&=\sin \left (t \right ) y+Q \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.329 |
|
| 18542 |
\begin{align*}
y^{\prime } x +3 y&=\frac {3}{x^{{3}/{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.331 |
|
| 18543 |
\begin{align*}
3 y x +2 y^{2}+y+\left (x^{2}+2 y x +x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.331 |
|
| 18544 |
\begin{align*}
y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.331 |
|
| 18545 |
\begin{align*}
y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.331 |
|
| 18546 |
\begin{align*}
x^{4} \left (y^{\prime }-y^{2}\right )&=a +b \,{\mathrm e}^{\frac {k}{x}}+c \,{\mathrm e}^{\frac {2 k}{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.331 |
|
| 18547 |
\begin{align*}
y^{\prime }&=\frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.332 |
|
| 18548 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime }+6 x^{2} y&=6 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.332 |
|
| 18549 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\sin \left (x^{2}\right ) \\
y \left (-1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.332 |
|
| 18550 |
\begin{align*}
y^{\prime }&=t y \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.332 |
|
| 18551 |
\begin{align*}
y^{\prime }&=\frac {t}{y-t^{2} y} \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.332 |
|
| 18552 |
\begin{align*}
x +y&=y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.333 |
|
| 18553 |
\begin{align*}
\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.333 |
|
| 18554 |
\begin{align*}
y^{\prime }&=\frac {x +y}{x} \\
y \left (3\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.333 |
|
| 18555 |
\begin{align*}
x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.334 |
|
| 18556 | \begin{align*}
y^{\prime }&=\frac {y \,{\mathrm e}^{x +y}}{x^{2}+2} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.335 |
|
| 18557 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +8 \left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.335 |
|
| 18558 |
\begin{align*}
x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z&=0 \\
z \left (1\right ) &= 0 \\
z^{\prime }\left (1\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.335 |
|
| 18559 |
\begin{align*}
\left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.335 |
|
| 18560 |
\begin{align*}
x^{\prime }&=x^{2}-1 \\
x \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.335 |
|
| 18561 |
\begin{align*}
v \left (2 u v^{2}-3\right )+\left (3 u^{2} v^{2}-3 u +4 v\right ) v^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.335 |
|
| 18562 |
\begin{align*}
y^{\prime }&=x \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.336 |
|
| 18563 |
\begin{align*}
\left (y-x^{2}\right ) y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.336 |
|
| 18564 |
\begin{align*}
y^{\prime } y+x&=\frac {y}{y^{2}+x^{2}}-\frac {x y^{\prime }}{y^{2}+x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.336 |
|
| 18565 |
\begin{align*}
y^{\prime }&=y^{2}-4 y-12 \\
y \left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.336 |
|
| 18566 |
\begin{align*}
\left (4 x^{2}-1\right ) y^{\prime \prime }+\left (4-\frac {2}{x}\right ) y^{\prime }+\frac {\left (-x^{2}+1\right ) y}{x^{2}+1}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.336 |
|
| 18567 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.337 |
|
| 18568 |
\begin{align*}
y^{\prime }&=y \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.338 |
|
| 18569 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=-1-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.338 |
|
| 18570 |
\begin{align*}
2 x^{2} y y^{\prime }&=x^{2} \left (2 x +1\right )-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.338 |
|
| 18571 |
\begin{align*}
y^{\prime }&=\cos \left (x -y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.338 |
|
| 18572 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-v \left (v +1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
2.339 |
|
| 18573 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +3 y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.339 |
|
| 18574 |
\begin{align*}
2 \sqrt {x}\, y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.340 |
|
| 18575 | \begin{align*}
x^{\prime }&={\mathrm e}^{x}-t \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.340 |
|
| 18576 |
\begin{align*}
y^{\prime }-a y&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.340 |
|
| 18577 |
\begin{align*}
\cos \left (y\right ) y^{\prime }&=-\frac {t \sin \left (y\right )}{t^{2}+1} \\
y \left (1\right ) &= \frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| 18578 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{4} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| 18579 |
\begin{align*}
y^{\prime }+y \sqrt {1+\sin \left (x \right )^{2}}&=x \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| 18580 |
\begin{align*}
y^{\prime } x -4 y&=x^{6} {\mathrm e}^{x} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.342 |
|
| 18581 |
\begin{align*}
{y^{\prime }}^{n}-f \left (x \right ) g \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| 18582 |
\begin{align*}
\left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| 18583 |
\begin{align*}
y^{\prime }&=2 y x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| 18584 |
\begin{align*}
\tan \left (x \right ) y^{\prime }&=y \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.343 |
|
| 18585 |
\begin{align*}
y^{\prime } x&=a +b y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.344 |
|
| 18586 |
\begin{align*}
y^{\prime }&=\frac {1+\sqrt {x}}{1+\sqrt {y}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.345 |
|
| 18587 |
\begin{align*}
y^{\prime \prime } x +\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.345 |
|
| 18588 |
\begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.345 |
|
| 18589 |
\begin{align*}
y^{3}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.346 |
|
| 18590 |
\begin{align*}
y^{\prime }&=1+2 x +y^{2}+2 x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.346 |
|
| 18591 |
\begin{align*}
\cos \left (y\right ) y^{\prime }&=-\frac {t \sin \left (y\right )}{t^{2}+1} \\
y \left (1\right ) &= \frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.346 |
|
| 18592 |
\begin{align*}
y \left (x +y\right )+\left (x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.346 |
|
| 18593 |
\begin{align*}
x^{k} y^{\prime }&=a \,x^{m}+b y^{n} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.346 |
|
| 18594 |
\begin{align*}
\left (x^{2}-a y\right ) {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.347 |
|
| 18595 | \begin{align*}
\ln \left (y^{\prime }\right )+y^{\prime } x +a&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.347 |
|
| 18596 |
\begin{align*}
\sec \left (y\right )^{2} y^{\prime }&=\tan \left (y\right )+2 x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
2.348 |
|
| 18597 |
\begin{align*}
x^{2} \left (a +y\right )^{2} y^{\prime }&=\left (x^{2}+1\right ) \left (y^{2}+a^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.348 |
|
| 18598 |
\begin{align*}
y^{\prime } y+x y^{2}-8 x&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.348 |
|
| 18599 |
\begin{align*}
x^{\prime }&=2 x+y-z+5 \sin \left (t \right ) \\
y^{\prime }&=y+z-10 \cos \left (t \right ) \\
z^{\prime }&=x+z+2 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.348 |
|
| 18600 |
\begin{align*}
2 t y+\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\
y \left (-3\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.349 |
|