| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 20501 |
\begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= -\frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.758 |
|
| 20502 |
\begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.761 |
|
| 20503 |
\begin{align*}
y^{\prime }&=1+\left (t -y\right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.761 |
|
| 20504 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime }&=\left (y+1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.763 |
|
| 20505 |
\begin{align*}
\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.763 |
|
| 20506 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.766 |
|
| 20507 |
\begin{align*}
a x y^{\prime }+2 y&=x y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.767 |
|
| 20508 |
\begin{align*}
y^{\prime }&=\frac {y}{2 \ln \left (y\right ) y+y-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.767 |
|
| 20509 |
\begin{align*}
y \,{\mathrm e}^{y x}-2 y^{3}+\left (x \,{\mathrm e}^{y x}-6 x y^{2}-2 y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.769 |
|
| 20510 |
\begin{align*}
x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+m y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.770 |
|
| 20511 |
\begin{align*}
y^{\prime }&=1-t +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.772 |
|
| 20512 |
\begin{align*}
3 t^{2}+4 y t +\left (2 t^{2}+2 y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.773 |
|
| 20513 |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) \cot \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.773 |
|
| 20514 |
\begin{align*}
2 y+y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.774 |
|
| 20515 |
\begin{align*}
\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-2 a^{2} x y y^{\prime }+y^{2}-a^{2} x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.774 |
|
| 20516 |
\begin{align*}
y^{\prime }+2 y x&=x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.775 |
|
| 20517 |
\begin{align*}
y^{\prime }+y \ln \left (y\right )&=y t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.775 |
|
| 20518 |
\begin{align*}
2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right )&=4 \cos \left (x \right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.777 |
|
| 20519 |
\begin{align*}
y^{\prime }&=x y^{2}-\frac {2 y}{x}-\frac {1}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.779 |
|
| 20520 |
\begin{align*}
y x -y^{2}-x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.780 |
|
| 20521 |
\begin{align*}
\frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}}&=1 \\
r \left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.780 |
|
| 20522 |
\begin{align*}
x \left (1-2 x^{2} y^{3}\right ) y^{\prime }+\left (1-2 x^{3} y^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.781 |
|
| 20523 |
\begin{align*}
y-y^{3}+\left (2 x y^{2}-x -a y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.781 |
|
| 20524 |
\begin{align*}
y^{\prime \prime }+\beta ^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.782 |
|
| 20525 |
\begin{align*}
t^{2} x^{\prime \prime }+x^{\prime } t -x&=0 \\
x \left (1\right ) &= 1 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.783 |
|
| 20526 |
\begin{align*}
y^{\prime }&=\frac {2 y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.783 |
|
| 20527 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}+y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
4.783 |
|
| 20528 |
\begin{align*}
y^{\prime }+3 x^{2} y&=3 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.785 |
|
| 20529 |
\begin{align*}
y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.786 |
|
| 20530 |
\begin{align*}
\left (3 x -1\right ) y^{\prime }&=6 y-10 \left (3 x -1\right )^{{1}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.786 |
|
| 20531 |
\begin{align*}
y^{\prime }&=\sin \left (t \right ) y+Q \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.786 |
|
| 20532 |
\begin{align*}
-\frac {3 y}{2}+y^{\prime }&=3 t +3 \,{\mathrm e}^{t} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.788 |
|
| 20533 |
\begin{align*}
\frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {x^{2}+y^{2}}}+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
4.790 |
|
| 20534 |
\begin{align*}
\cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.791 |
|
| 20535 |
\begin{align*}
y^{\prime }&=y-y^{3} \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
4.792 |
|
| 20536 |
\begin{align*}
x y^{\prime }&=x^{3}+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.792 |
|
| 20537 |
\begin{align*}
\left (x -x^{2} y-y^{3}\right ) y^{\prime }&=x^{3}-y+x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.795 |
|
| 20538 |
\begin{align*}
4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.796 |
|
| 20539 |
\begin{align*}
y^{\prime \prime }+t y^{\prime }-\ln \left (t \right ) y&=\cos \left (2 t \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
4.796 |
|
| 20540 |
\begin{align*}
y^{\prime }&=y^{2} \cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.796 |
|
| 20541 |
\begin{align*}
\left (2 x^{2} y^{3}+x^{2} y^{2}-2 x \right ) y^{\prime }-2 y-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.797 |
|
| 20542 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+4 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.798 |
|
| 20543 |
\begin{align*}
-1+{\mathrm e}^{y t} y+y \cos \left (y t \right )+\left (1+{\mathrm e}^{y t} t +t \cos \left (y t \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.798 |
|
| 20544 |
\begin{align*}
y^{\prime }+\frac {y}{x +1}&=-\frac {\left (x +1\right )^{3} y^{3}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.799 |
|
| 20545 |
\begin{align*}
y^{\prime }&=\frac {y+3}{1+3 x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.800 |
|
| 20546 |
\begin{align*}
2 y y^{\prime }&=y^{2}+t -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.800 |
|
| 20547 |
\begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.801 |
|
| 20548 |
\begin{align*}
x y^{2}+x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.801 |
|
| 20549 |
\begin{align*}
y^{\prime }&=-\frac {-\frac {1}{x}-\textit {\_F1} \left (y+\frac {1}{x}\right )}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.803 |
|
| 20550 |
\begin{align*}
t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.804 |
|
| 20551 |
\begin{align*}
\operatorname {a2} y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.806 |
|
| 20552 |
\begin{align*}
x y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.806 |
|
| 20553 |
\begin{align*}
\left (x^{2} y^{2}+x \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.806 |
|
| 20554 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.807 |
|
| 20555 |
\begin{align*}
x^{2} y^{\prime }&=\left (-1+y\right ) x +\left (-1+y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.809 |
|
| 20556 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \\
y \left (0\right ) &= -6 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.811 |
|
| 20557 |
\begin{align*}
y^{\prime \prime }-\lambda y&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (L \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.812 |
|
| 20558 |
\begin{align*}
y^{\prime }&=\cos \left (x \right )+\frac {y}{x} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.813 |
|
| 20559 |
\begin{align*}
x^{\prime } t +x&=2 t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.813 |
|
| 20560 |
\begin{align*}
{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.813 |
|
| 20561 |
\begin{align*}
\left (2-10 x^{2} y^{3}+3 y^{2}\right ) y^{\prime }&=x \left (1+5 y^{4}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.815 |
|
| 20562 |
\begin{align*}
y^{\prime }&=\frac {-\sin \left (2 y\right )+x \cos \left (2 y\right )+\cos \left (2 y\right ) x^{3}+\cos \left (2 y\right ) x^{4}+x +x^{3}+x^{4}}{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.815 |
|
| 20563 |
\begin{align*}
{y^{\prime }}^{3}+a_{0} {y^{\prime }}^{2}+a_{1} y^{\prime }+a_{2} +a_{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
4.816 |
|
| 20564 |
\begin{align*}
y^{\prime }&=\frac {y}{x \left (-1+y x +x y^{3}+x y^{4}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.816 |
|
| 20565 |
\begin{align*}
\frac {y^{\prime }}{\left (y+1\right )^{2}}-\frac {1}{x \left (y+1\right )}&=-\frac {3}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.819 |
|
| 20566 |
\begin{align*}
x y^{\prime }&=2 x^{2} y+\ln \left (y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.820 |
|
| 20567 |
\begin{align*}
\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.820 |
|
| 20568 |
\begin{align*}
\left ({\mathrm e}^{v}+1\right ) \cos \left (u \right )+{\mathrm e}^{v} \left (1+\sin \left (u \right )\right ) v^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.823 |
|
| 20569 |
\begin{align*}
{y^{\prime }}^{2} x +y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.824 |
|
| 20570 |
\begin{align*}
y^{\prime }&=\frac {\left (x^{{3}/{2}}+2 F \left (y-\frac {x^{3}}{6}\right )\right ) \sqrt {x}}{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.825 |
|
| 20571 |
\begin{align*}
x -x^{2}-y^{2}+\left (y+x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.826 |
|
| 20572 |
\begin{align*}
x y^{\prime }&=y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.826 |
|
| 20573 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.829 |
|
| 20574 |
\begin{align*}
y^{\prime }&=2 y-2 y t \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.829 |
|
| 20575 |
\begin{align*}
\left (x +2 y+2 x^{2} y^{3}+x y^{4}\right ) y^{\prime }+y^{5}+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.829 |
|
| 20576 |
\begin{align*}
y^{\prime }&=\left (-\ln \left (y\right )+1+x^{2}+x^{3}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.830 |
|
| 20577 |
\begin{align*}
\left ({\mathrm e}^{x}+{\mathrm e}^{-x}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.831 |
|
| 20578 |
\begin{align*}
y^{\prime }&=-\frac {y}{t}+2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.832 |
|
| 20579 |
\begin{align*}
x y^{\prime \prime }&=y^{\prime }-2 {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.835 |
|
| 20580 |
\begin{align*}
2 y t +\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\
y \left (1\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.836 |
|
| 20581 |
\begin{align*}
{\mathrm e}^{x} \cos \left (y\right )+x -\left ({\mathrm e}^{x} \sin \left (y\right )+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.836 |
|
| 20582 |
\begin{align*}
\left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+y x -x^{2}\right ) y^{\prime }+y \left (-x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.837 |
|
| 20583 |
\begin{align*}
\left (t +1\right ) x^{\prime }+x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.839 |
|
| 20584 |
\begin{align*}
-y+y^{\prime }&={\mathrm e}^{t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.839 |
|
| 20585 |
\begin{align*}
y^{\prime }&=\frac {y \ln \left (x -1\right )+x^{4}+x^{3}+x^{2} y^{2}+x y^{2}}{\ln \left (x -1\right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.840 |
|
| 20586 |
\begin{align*}
\sqrt {t}\, \sin \left (t \right ) y+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.841 |
|
| 20587 |
\begin{align*}
\sin \left (\theta \right ) \theta ^{\prime }+\cos \left (\theta \right )-t \,{\mathrm e}^{-t}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.842 |
|
| 20588 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.842 |
|
| 20589 |
\begin{align*}
x^{\prime }&=\frac {x+2 t}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.842 |
|
| 20590 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{2}-2 x_{3}+3 x_{4}+2 x_{5} \\
x_{2}^{\prime }&=8 x_{1}+6 x_{2}+4 x_{3}-8 x_{4}-16 x_{5} \\
x_{3}^{\prime }&=-8 x_{1}-8 x_{2}-6 x_{3}+8 x_{4}-16 x_{5} \\
x_{4}^{\prime }&=8 x_{1}+7 x_{2}+4 x_{3}-9 x_{4}-16 x_{5} \\
x_{5}^{\prime }&=-3 x_{1}-5 x_{2}-3 x_{3}+5 x_{4}+7 x_{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.843 |
|
| 20591 |
\begin{align*}
y^{\prime \prime }&=a^{2}+k^{2} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.845 |
|
| 20592 |
\begin{align*}
y^{\prime }&=y^{2}-2 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
4.849 |
|
| 20593 |
\begin{align*}
x y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.850 |
|
| 20594 |
\begin{align*}
2 y^{\prime }+x y^{\prime \prime }&=-y^{2}+x^{2} y^{\prime } \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
4.851 |
|
| 20595 |
\begin{align*}
3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
4.853 |
|
| 20596 |
\begin{align*}
y^{\prime }&=3 y \left (-2+y\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.853 |
|
| 20597 |
\begin{align*}
\left (20 x^{2}+8 y x +4 y^{2}+3 y^{3}\right ) y+4 \left (x^{2}+y x +y^{2}+y^{3}\right ) x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.853 |
|
| 20598 |
\begin{align*}
t^{2} x^{\prime \prime }+a t x^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.855 |
|
| 20599 |
\begin{align*}
x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.857 |
|
| 20600 |
\begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.858 |
|