| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 20501 |
\begin{align*}
\sqrt {-x^{2}+1}\, y^{2} y^{\prime }&=\arcsin \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.966 |
|
| 20502 |
\begin{align*}
x^{2} y+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.966 |
|
| 20503 |
\begin{align*}
\left (x -a \right ) \left (-b +x \right ) y^{\prime }&=\left (x -a \right ) \left (-b +x \right )+\left (2 x -a -b \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.967 |
|
| 20504 |
\begin{align*}
u^{\prime }&=a \sqrt {1+u^{2}} \\
u \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.967 |
|
| 20505 |
\begin{align*}
\left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.968 |
|
| 20506 |
\begin{align*}
y&=2 y^{\prime } x +\ln \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.969 |
|
| 20507 |
\begin{align*}
2 t +y^{3}+\left (3 t y^{2}+4\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.970 |
|
| 20508 |
\begin{align*}
y^{\prime }&=y-\mu y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.970 |
|
| 20509 |
\begin{align*}
p^{\prime }&=\frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.971 |
|
| 20510 |
\begin{align*}
y^{\prime }-\frac {3 y}{x}&=x^{3} \\
y \left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.971 |
|
| 20511 |
\begin{align*}
y^{\prime }&=x +y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.971 |
|
| 20512 |
\begin{align*}
y y^{\prime \prime }&=\ln \left (y\right ) y^{2}+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.973 |
|
| 20513 |
\begin{align*}
\left (x^{2}+1\right ) y y^{\prime }+4&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.973 |
|
| 20514 |
\begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.974 |
|
| 20515 |
\begin{align*}
4 y^{\prime \prime }+4 \tan \left (x \right ) y^{\prime }-\left (5 \tan \left (x \right )^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.974 |
|
| 20516 |
\begin{align*}
2 y y^{\prime \prime }-3 {y^{\prime }}^{2}&=4 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.974 |
|
| 20517 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\left (9 x^{2}-3 x -4\right ) {\mathrm e}^{-x} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
3.974 |
|
| 20518 |
\begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.976 |
|
| 20519 |
\begin{align*}
v^{\prime }&=t^{2} v-2-2 v+t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.977 |
|
| 20520 |
\begin{align*}
r^{\prime }+\left (r-\frac {1}{r}\right ) \theta &=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.978 |
|
| 20521 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.978 |
|
| 20522 |
\begin{align*}
x^{4} y^{\prime }+x^{3} y+\csc \left (y x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.978 |
|
| 20523 |
\begin{align*}
{\mathrm e}^{4 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.981 |
|
| 20524 |
\begin{align*}
y^{\prime \prime }+10 y&=0 \\
y \left (0\right ) &= \pi \\
y^{\prime }\left (0\right ) &= \pi ^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.983 |
|
| 20525 |
\begin{align*}
1+s^{2}-\sqrt {t}\, s^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.983 |
|
| 20526 |
\begin{align*}
y^{\prime }&=2 x +1+y^{2}-2 x^{2} y+x^{4}+y^{3}-3 y^{2} x^{2}+3 x^{4} y-x^{6} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.985 |
|
| 20527 |
\begin{align*}
y^{\prime }&=\frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 x y^{2}+64 y^{3}}{\left (4 x -5\right )^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.986 |
|
| 20528 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.989 |
|
| 20529 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 \,{\mathrm e}^{x} y^{\prime } x +3 \cos \left (x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.990 |
|
| 20530 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.991 |
|
| 20531 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.991 |
|
| 20532 |
\begin{align*}
x \ln \left (x \right ) y^{\prime }+y&=2 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.991 |
|
| 20533 |
\begin{align*}
{y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.992 |
|
| 20534 |
\begin{align*}
y^{\prime }+\frac {2 x \sin \left (y\right )+y^{3} {\mathrm e}^{x}}{\cos \left (y\right ) x^{2}+3 y^{2} {\mathrm e}^{x}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.992 |
|
| 20535 |
\begin{align*}
\cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.992 |
|
| 20536 |
\begin{align*}
y^{\prime }+y x&=4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.993 |
|
| 20537 |
\begin{align*}
y^{\prime } x&=\left (x +1\right ) y^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.994 |
|
| 20538 |
\begin{align*}
y^{\prime } t&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.996 |
|
| 20539 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.996 |
|
| 20540 |
\begin{align*}
y \left (-y+y^{\prime } x \right )^{2}&=y-2 y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.996 |
|
| 20541 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.997 |
|
| 20542 |
\begin{align*}
y-y^{\prime } x&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.997 |
|
| 20543 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.998 |
|
| 20544 |
\begin{align*}
y^{\prime }&=-3 y+{\mathrm e}^{-2 t}+t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.998 |
|
| 20545 |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.999 |
|
| 20546 |
\begin{align*}
y^{\prime }+8 x^{3} y^{3}+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.000 |
|
| 20547 |
\begin{align*}
2 \left (1+y\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+y^{2}+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.001 |
|
| 20548 |
\begin{align*}
{y^{\prime \prime }}^{2}+2 y^{\prime \prime } x -y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.001 |
|
| 20549 |
\begin{align*}
x^{2}+y^{2}-x^{2} y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.001 |
|
| 20550 |
\begin{align*}
y^{\prime }&=\sqrt {y^{2}-9} \\
y \left (5\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.003 |
|
| 20551 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.003 |
|
| 20552 |
\begin{align*}
3 y^{\prime } x -3 x y^{4} \ln \left (x \right )-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.003 |
|
| 20553 |
\begin{align*}
y y^{\prime }&=x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.004 |
|
| 20554 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x^{4} y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.004 |
|
| 20555 |
\begin{align*}
\left (a +b \cos \left (2 x \right )\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.006 |
|
| 20556 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.006 |
|
| 20557 |
\begin{align*}
y^{2}+y x -y^{\prime } x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.006 |
|
| 20558 |
\begin{align*}
y^{\prime }&={\mathrm e}^{2 x -3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.006 |
|
| 20559 |
\begin{align*}
y^{\prime }&=\frac {2 y}{x}-\sqrt {3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.007 |
|
| 20560 |
\begin{align*}
x^{\prime }&=\frac {x-t}{x-t +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.007 |
|
| 20561 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.009 |
|
| 20562 |
\begin{align*}
y^{\prime }&=\frac {x +1+y^{4}-2 y^{2} x^{2}+x^{4}+y^{6}-3 x^{2} y^{4}+3 y^{2} x^{4}-x^{6}}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.010 |
|
| 20563 |
\begin{align*}
z^{\prime }+7 y-9 z&={\mathrm e}^{x} \\
y^{\prime }-y-3 z&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.010 |
|
| 20564 |
\begin{align*}
y^{\prime }&=\frac {y}{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.011 |
|
| 20565 |
\begin{align*}
y^{\prime }+\tan \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.013 |
|
| 20566 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=10 x +12 \\
y \left (1\right ) &= 6 \\
y^{\prime }\left (1\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.013 |
|
| 20567 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (\frac {\pi }{3}\right ) &= 2 \\
y^{\prime }\left (\frac {\pi }{3}\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.013 |
|
| 20568 |
\begin{align*}
\left (x^{2}-1\right ) y+\left (1+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.013 |
|
| 20569 |
\begin{align*}
y^{\prime }-\frac {a y}{x}&=\frac {x +1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.015 |
|
| 20570 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.017 |
|
| 20571 |
\begin{align*}
y^{\prime } \left (x^{3}+1\right )^{{2}/{3}}+\left (y^{3}+1\right )^{{2}/{3}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.018 |
|
| 20572 |
\begin{align*}
x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.018 |
|
| 20573 |
\begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.018 |
|
| 20574 |
\begin{align*}
y^{\prime }-4 y&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.019 |
|
| 20575 |
\begin{align*}
\left (\cos \left (x \right )+1\right ) y^{\prime }+\sin \left (x \right ) \left (\sin \left (x \right )+\cos \left (x \right ) \sin \left (x \right )-y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.021 |
|
| 20576 |
\begin{align*}
3 x^{2} {\mathrm e}^{y}-2 x +\left (x^{3} {\mathrm e}^{y}-\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.021 |
|
| 20577 |
\begin{align*}
5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.024 |
|
| 20578 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +36 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.026 |
|
| 20579 |
\begin{align*}
y-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.026 |
|
| 20580 |
\begin{align*}
\frac {2 y^{{3}/{2}}+1}{\sqrt {x}}+\left (3 \sqrt {x}\, \sqrt {y}-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.027 |
|
| 20581 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=x^{3} {\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.028 |
|
| 20582 |
\begin{align*}
\tan \left (y\right )&=\left (3 x +4\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.029 |
|
| 20583 |
\begin{align*}
y^{\prime }+\frac {y}{\sin \left (x \right )}-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.029 |
|
| 20584 |
\begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.030 |
|
| 20585 |
\begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
4.031 |
|
| 20586 |
\begin{align*}
\cos \left (y\right ) \sin \left (x \right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.031 |
|
| 20587 |
\begin{align*}
y^{\prime }-\frac {2 y}{t}&=2 t^{2} \\
y \left (-2\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.032 |
|
| 20588 |
\begin{align*}
3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.035 |
|
| 20589 |
\begin{align*}
x^{2} y^{\prime }+y x +1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.035 |
|
| 20590 |
\begin{align*}
y \cos \left (y x \right )+y-x +\left (x \cos \left (y x \right )+x -y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.037 |
|
| 20591 |
\begin{align*}
\left (x +\frac {x}{x^{2}+y^{2}}\right ) y^{\prime }+y-\frac {y}{x^{2}+y^{2}}&=0 \\
y \left (1\right ) &= \sqrt {3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.037 |
|
| 20592 |
\begin{align*}
4 y+3 \left (2 x -1\right ) \left (y^{\prime }+y^{4}\right )&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.037 |
|
| 20593 |
\begin{align*}
y^{\prime }&=-\frac {y}{1+t}+t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.038 |
|
| 20594 |
\begin{align*}
t^{2} y^{\prime \prime }-5 y^{\prime } t +5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.042 |
|
| 20595 |
\begin{align*}
y^{\prime } \ln \left (x -y\right )&=1+\ln \left (x -y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.042 |
|
| 20596 |
\begin{align*}
y^{\prime }&=4 x^{3} y-y \\
y \left (1\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.043 |
|
| 20597 |
\begin{align*}
y^{\prime }&=\frac {y x +3 x -y-3}{y x -2 x +4 y-8} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.043 |
|
| 20598 |
\begin{align*}
\left (\ln \left (y\right )+2 x -1\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.044 |
|
| 20599 |
\begin{align*}
y^{\prime \prime } x +\left (2 x +3\right ) y^{\prime }+8 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.045 |
|
| 20600 |
\begin{align*}
\left (3 x +8\right ) \left (4+y^{2}\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.046 |
|