| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 19501 |
\begin{align*}
y^{\prime }&=\frac {5 x^{2}-y x +y^{2}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.792 |
|
| 19502 |
\begin{align*}
y^{\prime }-\frac {y}{-x^{2}+1}&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.792 |
|
| 19503 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime }+3 y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.793 |
|
| 19504 |
\begin{align*}
x -2 y x +{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.794 |
|
| 19505 |
\begin{align*}
y^{\prime }-y x&=-x^{2}+1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.794 |
|
| 19506 |
\begin{align*}
y^{\prime } x&=5 y+x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.795 |
|
| 19507 |
\begin{align*}
y^{2}-y^{2} \cos \left (x \right )+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.795 |
|
| 19508 |
\begin{align*}
y^{\prime }-y \sin \left (x \right )&=2 \sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.796 |
|
| 19509 |
\begin{align*}
y^{\prime } x +a +x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.796 |
|
| 19510 |
\begin{align*}
x^{\prime }&=-t x \\
x \left (0\right ) &= {\mathrm e} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.796 |
|
| 19511 |
\begin{align*}
x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.797 |
|
| 19512 |
\begin{align*}
3 x^{2} y-y^{3}-\left (3 x y^{2}-x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.797 |
|
| 19513 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-v^{2}+x^{2}\right ) y-f \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.798 |
|
| 19514 |
\begin{align*}
4 \sinh \left (4 y\right ) y^{\prime }&=6 \cosh \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.798 |
|
| 19515 |
\begin{align*}
y-2 y x +x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.799 |
|
| 19516 |
\begin{align*}
x \ln \left (x \right ) y^{\prime }+y-a x \left (1+\ln \left (x \right )\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.800 |
|
| 19517 |
\begin{align*}
x^{2} y^{\prime }&=y-y x \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.801 |
|
| 19518 | \begin{align*}
x +y-2+\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.802 |
|
| 19519 |
\begin{align*}
3 x^{2} y y^{\prime }+1+2 x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.803 |
|
| 19520 |
\begin{align*}
y^{\prime } x +a y+b \,x^{n}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.803 |
|
| 19521 |
\begin{align*}
2 y+\left (x +1\right ) y^{\prime }&=\frac {\sin \left (x \right )}{x +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.806 |
|
| 19522 |
\begin{align*}
2 y-x y \ln \left (x \right )-2 x \ln \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.806 |
|
| 19523 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (2 n +1\right ) \cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\left (v +n +1\right ) \left (v -n \right ) y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.806 |
|
| 19524 |
\begin{align*}
y^{2} \left (x^{2}+2\right )+\left (x^{3}+y^{3}\right ) \left (y-y^{\prime } x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.807 |
|
| 19525 |
\begin{align*}
\left (\frac {{\mathrm e}^{-y^{2}}}{2}-y x \right ) y^{\prime }-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.807 |
|
| 19526 |
\begin{align*}
{\mathrm e}^{x}+y \,{\mathrm e}^{y x}+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.809 |
|
| 19527 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=2 \delta \left (-1+t \right )-\delta \left (t -2\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| 19528 |
\begin{align*}
\sin \left (x \right ) y^{\prime }&=y \ln \left (y\right ) \\
y \left (\frac {\pi }{3}\right ) &= {\mathrm e} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| 19529 |
\begin{align*}
\left (x +1\right ) y^{\prime }+y x&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| 19530 |
\begin{align*}
x^{2} y+\left (x +1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| 19531 |
\begin{align*}
x^{2} \left (1-y\right ) y^{\prime }+\left (x +1\right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.810 |
|
| 19532 |
\begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
2.810 |
|
| 19533 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (-2\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.811 |
|
| 19534 |
\begin{align*}
-2 \left (\cos \left (x \right )+1\right ) \sec \left (x \right ) y-\left (2+3 \cos \left (x \right )\right ) \csc \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.812 |
|
| 19535 |
\begin{align*}
y^{\prime }&=1+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.813 |
|
| 19536 |
\begin{align*}
x^{\prime \prime }-\tan \left (t \right ) x^{\prime }+x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.818 |
|
| 19537 | \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +a y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.821 |
|
| 19538 |
\begin{align*}
y-x y^{2} \ln \left (x \right )+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.821 |
|
| 19539 |
\begin{align*}
y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.821 |
|
| 19540 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}&=5 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.822 |
|
| 19541 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.822 |
|
| 19542 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-v \left (v -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.822 |
|
| 19543 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= {\frac {1}{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.822 |
|
| 19544 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x} \sin \left (x \right )+\cot \left (x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.823 |
|
| 19545 |
\begin{align*}
\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}}&=-x \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.823 |
|
| 19546 |
\begin{align*}
y^{\prime }-f \left (x \right )^{1-n} g^{\prime }\left (x \right ) y^{n} \left (a g \left (x \right )+b \right )^{-n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-g^{\prime }\left (x \right ) f \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.823 |
|
| 19547 |
\begin{align*}
y^{2}-1+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.825 |
|
| 19548 |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.825 |
|
| 19549 |
\begin{align*}
x \left (1+y^{2}\right )+\left (1+2 y\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.826 |
|
| 19550 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.826 |
|
| 19551 |
\begin{align*}
3 y^{2} y^{\prime } x&=2 x -y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.827 |
|
| 19552 |
\begin{align*}
x \left (x^{2}-y^{2}-x \right )-y \left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.827 |
|
| 19553 |
\begin{align*}
y^{\prime } y-x y^{2}&=6 x \,{\mathrm e}^{4 x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.828 |
|
| 19554 |
\begin{align*}
y-x y^{2} \ln \left (x \right )+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.828 |
|
| 19555 |
\begin{align*}
r^{\prime }+\left (r-\frac {1}{r}\right ) \theta &=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.829 |
|
| 19556 | \begin{align*}
2 y x +\left (x^{2}-y\right ) y^{\prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.829 |
|
| 19557 |
\begin{align*}
2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.829 |
|
| 19558 |
\begin{align*}
\left (x +1\right ) y^{2}+y+\left (2 y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.829 |
|
| 19559 |
\begin{align*}
y^{\prime } y&=y+x^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.829 |
|
| 19560 |
\begin{align*}
1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.830 |
|
| 19561 |
\begin{align*}
y-\cos \left (x \right )^{2}+\cos \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.830 |
|
| 19562 |
\begin{align*}
y^{\prime } x +y&=x^{2} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.831 |
|
| 19563 |
\begin{align*}
y+\left (a +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.832 |
|
| 19564 |
\begin{align*}
b y+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.832 |
|
| 19565 |
\begin{align*}
y^{\prime }&=\frac {2 y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.832 |
|
| 19566 |
\begin{align*}
y^{\prime }-y^{2}+\left (x^{2}+1\right ) y-2 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.832 |
|
| 19567 |
\begin{align*}
4 y x +\left (3 x^{2}+5 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.833 |
|
| 19568 |
\begin{align*}
y^{\prime } x +y&=x y^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.833 |
|
| 19569 |
\begin{align*}
x^{\prime }&=-t^{2} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.833 |
|
| 19570 |
\begin{align*}
y^{\prime }&=\frac {2 y^{2}+x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}}{2 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.835 |
|
| 19571 |
\begin{align*}
t x^{\prime }&=6 \,{\mathrm e}^{2 t} t +x \left (2 t -1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.836 |
|
| 19572 |
\begin{align*}
y^{\prime }&=\frac {-x +3}{y+5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.837 |
|
| 19573 |
\begin{align*}
\sqrt {1+{y^{\prime }}^{2}}+x {y^{\prime }}^{2}+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.838 |
|
| 19574 |
\begin{align*}
y^{\prime }-y \ln \left (2\right )&=2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.838 |
|
| 19575 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y&=6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.839 |
|
| 19576 | \begin{align*}
y^{3} x^{4}+y+\left (x^{5} y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 2.839 |
|
| 19577 |
\begin{align*}
\ln \left (y^{\prime }\right )+a \left (-y+y^{\prime } x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.839 |
|
| 19578 |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.839 |
|
| 19579 |
\begin{align*}
y^{\prime } x&=2 x -6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.839 |
|
| 19580 |
\begin{align*}
-\frac {1}{x^{5}}+\frac {1}{x^{3}}&=\left (2 y^{4}-6 y^{9}\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.839 |
|
| 19581 |
\begin{align*}
y^{\prime } x -3 y&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.839 |
|
| 19582 |
\begin{align*}
a_{0} \left (x \right ) y^{\prime \prime }+a_{1} \left (x \right ) y^{\prime }+a_{2} \left (x \right ) y&=f \left (x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.839 |
|
| 19583 |
\begin{align*}
\left (x -y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.841 |
|
| 19584 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=\sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.841 |
|
| 19585 |
\begin{align*}
{\mathrm e}^{x}+y+\left (x -2 \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.841 |
|
| 19586 |
\begin{align*}
2 x +\tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.841 |
|
| 19587 |
\begin{align*}
y^{\prime }&=x +\frac {y^{2}}{2} \\
y \left (-2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.842 |
|
| 19588 |
\begin{align*}
y^{\prime \prime }&=\cos \left (x \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.842 |
|
| 19589 |
\begin{align*}
{\mathrm e}^{x} \left (y^{2} x^{2}+2 x y^{2}\right )+6 x +\left (2 x^{2} y \,{\mathrm e}^{x}+2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.843 |
|
| 19590 |
\begin{align*}
y^{\prime }&=x +y \\
y \left (1\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.843 |
|
| 19591 |
\begin{align*}
y^{\prime }&=\frac {x \left (x^{2}+1\right ) y^{5}}{6} \\
y \left (0\right ) &= -2^{{1}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.843 |
|
| 19592 |
\begin{align*}
\left (y^{2} x^{2}-1\right ) y^{\prime }+2 x y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.844 |
|
| 19593 |
\begin{align*}
t +y-t y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.845 |
|
| 19594 |
\begin{align*}
x^{2} y^{\prime }&=y x +x^{2} {\mathrm e}^{\frac {y}{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.846 |
|
| 19595 |
\begin{align*}
y^{\prime }&=\frac {x y^{2}}{\sqrt {x^{2}+1}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.846 |
|
| 19596 | \begin{align*}
y^{\prime \prime } x -y^{\prime }-x^{3} y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.848 |
|
| 19597 |
\begin{align*}
x^{\prime }+2 x&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.848 |
|
| 19598 |
\begin{align*}
y^{\prime }&=y-\mu y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.851 |
|
| 19599 |
\begin{align*}
\cos \left (x \right ) y^{\prime }&=y-\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.851 |
|
| 19600 |
\begin{align*}
\left (x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }-6 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.852 |
|