| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 16501 |
\begin{align*}
y-a +x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.612 |
|
| 16502 |
\begin{align*}
y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.612 |
|
| 16503 |
\begin{align*}
y^{\prime } x +2 y&=\frac {2}{x^{2}}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.614 |
|
| 16504 |
\begin{align*}
x^{\prime }&=2 x-5 y+4 \\
y^{\prime }&=3 x-7 y+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.614 |
|
| 16505 |
\begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y&=2 \ln \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.614 |
|
| 16506 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.614 |
|
| 16507 |
\begin{align*}
y^{\prime } \sin \left (y\right )&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.615 |
|
| 16508 |
\begin{align*}
\left (\cos \left (\lambda x \right ) a +b \right ) y^{\prime }&=y^{2}+c \cos \left (\mu x \right ) y-d^{2}+c d \cos \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.615 |
|
| 16509 |
\begin{align*}
y^{\prime } x +y&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.615 |
|
| 16510 |
\begin{align*}
y^{\prime }&=2 y^{3}+t^{2} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.615 |
|
| 16511 |
\begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.616 |
|
| 16512 |
\begin{align*}
y^{\prime }+y x&=x^{3} y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.616 |
|
| 16513 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }&={\mathrm e}^{x}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.617 |
|
| 16514 |
\begin{align*}
y^{\prime }&=3 y \left (y-2\right ) \\
y \left (-2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
1.618 |
|
| 16515 |
\begin{align*}
v+\left (2 x +1-v x \right ) v^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.618 |
|
| 16516 |
\begin{align*}
6 y^{\prime \prime }+2 y^{\prime }+y&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.619 |
|
| 16517 |
\begin{align*}
y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.619 |
|
| 16518 | \begin{align*}
x^{\prime }&=2 x+4 y-2 z-2 \sinh \left (t \right ) \\
y^{\prime }&=4 x+2 y-2 z+10 \cosh \left (t \right ) \\
z^{\prime }&=-x+3 y+z+5 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.619 |
|
| 16519 |
\begin{align*}
t^{2} x^{\prime \prime }+3 t x^{\prime }-3 x&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.619 |
|
| 16520 |
\begin{align*}
-a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.619 |
|
| 16521 |
\begin{align*}
x u^{\prime \prime }-\left ({\mathrm e}^{x} x^{2}+1\right ) u^{\prime }-x^{2} {\mathrm e}^{x} u&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.620 |
|
| 16522 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.621 |
|
| 16523 |
\begin{align*}
y&=y^{\prime } x -{y^{\prime }}^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.621 |
|
| 16524 |
\begin{align*}
x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.621 |
|
| 16525 |
\begin{align*}
\frac {r^{\prime }}{r}&=\tan \left (\theta \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.621 |
|
| 16526 |
\begin{align*}
y^{\prime }&=\frac {2 y x +2 x}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.622 |
|
| 16527 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-x +y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.622 |
|
| 16528 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
y \left (2\right ) &= 3 \\
y^{\prime }\left (2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.622 |
|
| 16529 |
\begin{align*}
y^{\prime }&=y \cos \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.622 |
|
| 16530 |
\begin{align*}
y^{\prime }&=\frac {x^{2}-2 x^{2} y+2}{x^{3}} \\
y \left (1\right ) &= {\frac {3}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.623 |
|
| 16531 |
\begin{align*}
2 y^{\prime \prime }&={y^{\prime }}^{3} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.623 |
|
| 16532 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x -1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.623 |
|
| 16533 |
\begin{align*}
y^{\prime }&=t^{2}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.623 |
|
| 16534 |
\begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }-y&=x +\frac {1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.624 |
|
| 16535 |
\begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=a \,x^{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.625 |
|
| 16536 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.626 |
|
| 16537 | \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 1.627 |
|
| 16538 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }&=4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.628 |
|
| 16539 |
\begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.628 |
|
| 16540 |
\begin{align*}
y^{\prime }&=\sqrt {x +y+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.629 |
|
| 16541 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.629 |
|
| 16542 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.630 |
|
| 16543 |
\begin{align*}
{y^{\prime }}^{2}-\left (4 y+1\right ) y^{\prime }+\left (4 y+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.630 |
|
| 16544 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+x}{y-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.631 |
|
| 16545 |
\begin{align*}
y^{\prime \prime }&=a^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.631 |
|
| 16546 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=x^{2} y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.631 |
|
| 16547 |
\begin{align*}
2 y+y^{\prime }&=x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.631 |
|
| 16548 |
\begin{align*}
2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.631 |
|
| 16549 |
\begin{align*}
x +2 y-1+\left (2 x +4 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.631 |
|
| 16550 |
\begin{align*}
x \,{\mathrm e}^{y} y^{\prime }&=2 \,{\mathrm e}^{y}+2 x^{3} {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.632 |
|
| 16551 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.632 |
|
| 16552 |
\begin{align*}
y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.632 |
|
| 16553 |
\begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (2+4 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.632 |
|
| 16554 |
\begin{align*}
x^{2}-y+\left (y^{2} x^{2}+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.632 |
|
| 16555 |
\begin{align*}
-y+y^{\prime }&=4 t \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.632 |
|
| 16556 | \begin{align*}
y^{\prime \prime } x +2 y^{\prime }-y x -{\mathrm e}^{x}&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 1.634 |
|
| 16557 |
\begin{align*}
x^{n +1} y^{\prime }&=x^{2 n} a y^{2}+b \,x^{n} y+c \,x^{m}+d \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.634 |
|
| 16558 |
\begin{align*}
y^{\prime }&=2 y-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.634 |
|
| 16559 |
\begin{align*}
y^{\prime }&=t y \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.634 |
|
| 16560 |
\begin{align*}
\frac {y}{t}+y^{\prime }&=3 \cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| 16561 |
\begin{align*}
y^{\prime }&=\frac {x}{x^{2}+y^{3}+y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| 16562 |
\begin{align*}
y^{\prime }&=a x y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| 16563 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| 16564 |
\begin{align*}
x_{1}^{\prime }&=-8 x_{1}-16 x_{2}-16 x_{3}-17 x_{4} \\
x_{2}^{\prime }&=-2 x_{1}-10 x_{2}-8 x_{3}-7 x_{4} \\
x_{3}^{\prime }&=-2 x_{1}-2 x_{3}-3 x_{4} \\
x_{4}^{\prime }&=6 x_{1}+14 x_{2}+14 x_{3}+14 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| 16565 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime }+3 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| 16566 |
\begin{align*}
t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=4 t^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.635 |
|
| 16567 |
\begin{align*}
b \tan \left (x \right )^{2} y-2 \csc \left (2 x \right ) \left (1-a \sin \left (x \right )^{2}\right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.636 |
|
| 16568 |
\begin{align*}
3 y y^{\prime \prime }+y&=5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.636 |
|
| 16569 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.637 |
|
| 16570 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.637 |
|
| 16571 |
\begin{align*}
2 y^{\prime } x -3 y&=9 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.638 |
|
| 16572 |
\begin{align*}
y^{2} y^{\prime }+2 x y^{3}&=6 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.638 |
|
| 16573 |
\begin{align*}
e^{\prime }&=-\frac {e}{r c} \\
e \left (4\right ) &= e_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.638 |
|
| 16574 |
\begin{align*}
x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.638 |
|
| 16575 |
\begin{align*}
x^{4} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a \,x^{n -1}+a b \,x^{-2+n}+b^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.638 |
|
| 16576 | \begin{align*}
y^{\prime }&=y+{\mathrm e}^{-t} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.638 |
|
| 16577 |
\begin{align*}
y^{\prime }&=4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.638 |
|
| 16578 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=\frac {50}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.638 |
|
| 16579 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x +y}+x^{2} {\mathrm e}^{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.638 |
|
| 16580 |
\begin{align*}
-a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.638 |
|
| 16581 |
\begin{align*}
y^{\prime }&=\frac {t^{2}+1}{3 y-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.639 |
|
| 16582 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.639 |
|
| 16583 |
\begin{align*}
\left (x -1-y^{2}\right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.639 |
|
| 16584 |
\begin{align*}
x \left (1+y\right ) y^{\prime }-\left (1-x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.639 |
|
| 16585 |
\begin{align*}
y^{2} \left (y^{\prime }-1\right )&=\left (2-y^{\prime }\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.639 |
|
| 16586 |
\begin{align*}
-\frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\
y \left (0\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.640 |
|
| 16587 |
\begin{align*}
2 x \tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.640 |
|
| 16588 |
\begin{align*}
b y+a x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.640 |
|
| 16589 |
\begin{align*}
y^{\prime }&={\mathrm e}^{2 x -3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.641 |
|
| 16590 |
\begin{align*}
y+y^{\prime }&=5 \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.641 |
|
| 16591 |
\begin{align*}
y^{\prime } x -n y&=x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.642 |
|
| 16592 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (x +1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.642 |
|
| 16593 |
\begin{align*}
2 t y+y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.642 |
|
| 16594 |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) \cot \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.643 |
|
| 16595 | \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x -y}}{{\mathrm e}^{x}+1} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.643 |
|
| 16596 |
\begin{align*}
\left (2 x -1\right ) y^{\prime }-2 y&=\frac {1-4 x}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.643 |
|
| 16597 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & \pi \le t <2 \pi \\ 0 & \operatorname {otherwise} \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.644 |
|
| 16598 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.644 |
|
| 16599 |
\begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{-3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.644 |
|
| 16600 |
\begin{align*}
y^{\prime }+a y&=k \,{\mathrm e}^{b x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.644 |
|