| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15701 |
\begin{align*}
x^{2} y^{\prime \prime }&=2 y^{\prime } x +{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.576 |
|
| 15702 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.577 |
|
| 15703 |
\begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.578 |
|
| 15704 |
\begin{align*}
y^{\prime }&=x^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.578 |
|
| 15705 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.579 |
|
| 15706 |
\begin{align*}
x \left (a x +1\right ) y^{\prime }+a -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.579 |
|
| 15707 |
\begin{align*}
a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.579 |
|
| 15708 |
\begin{align*}
4 y^{\prime \prime }+4 y^{\prime }-3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.579 |
|
| 15709 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.579 |
|
| 15710 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x^{4} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.579 |
|
| 15711 |
\begin{align*}
y^{\prime \prime }+\left (2 \,{\mathrm e}^{x}-1\right ) y^{\prime }+y \,{\mathrm e}^{2 x}&={\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.580 |
|
| 15712 |
\begin{align*}
y^{\prime }&=\sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.582 |
|
| 15713 |
\begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.582 |
|
| 15714 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.582 |
|
| 15715 |
\begin{align*}
y^{\prime } x +\left (\sin \left (y\right )-3 \cos \left (y\right ) x^{2}\right ) \cos \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.584 |
|
| 15716 |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.584 |
|
| 15717 |
\begin{align*}
y^{\prime }-\frac {2 y}{x}&=\cos \left (x \right ) x^{2} \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.584 |
|
| 15718 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.584 |
|
| 15719 |
\begin{align*}
y^{\prime }&=1+x^{2}+y^{2}+y^{2} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.585 |
|
| 15720 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.585 |
|
| 15721 |
\begin{align*}
y^{\prime }-\frac {2 t y}{t^{2}+1}&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.585 |
|
| 15722 |
\begin{align*}
y y^{\prime }&=\left (x y^{2}+x \right ) {\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.587 |
|
| 15723 |
\begin{align*}
y^{\prime }&=2-\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.587 |
|
| 15724 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+\left (\tan \left (x \right )+\cot \left (x \right )\right ) y y^{\prime }+\left (\cos \left (x \right )^{2}-n^{2} \cot \left (x \right )^{2}\right ) y^{2} \ln \left (y\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.588 |
|
| 15725 |
\begin{align*}
y^{\prime }&=\frac {y}{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.589 |
|
| 15726 |
\begin{align*}
y^{\prime \prime }&=a \sqrt {b y^{2}+{y^{\prime }}^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.589 |
|
| 15727 |
\begin{align*}
y^{\prime } x&=2 x +3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.589 |
|
| 15728 |
\begin{align*}
\cot \left (\theta \right ) r^{\prime }&=r+b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.589 |
|
| 15729 |
\begin{align*}
2 \sqrt {x}\, y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.591 |
|
| 15730 |
\begin{align*}
x^{2} y^{\prime }&=\frac {4 x^{2}-x -2}{\left (x +1\right ) \left (1+y\right )} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.591 |
|
| 15731 |
\begin{align*}
x +2 y+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.591 |
|
| 15732 |
\begin{align*}
x^{2} y^{\prime }&=1-x^{2}+y^{2}-y^{2} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.592 |
|
| 15733 |
\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*} |
✓ |
✓ |
✓ |
✓ |
3.592 |
|
| 15734 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.593 |
|
| 15735 |
\begin{align*}
y+\left (y^{3}-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.593 |
|
| 15736 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.595 |
|
| 15737 |
\begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
3.595 |
|
| 15738 |
\begin{align*}
y y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.597 |
|
| 15739 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= {\frac {1}{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.598 |
|
| 15740 |
\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*} |
✓ |
✓ |
✓ |
✗ |
3.598 |
|
| 15741 |
\begin{align*}
y^{\prime }+\frac {\left (1+y\right ) \left (-1+y\right ) \left (y-2\right )}{x +1}&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.599 |
|
| 15742 |
\begin{align*}
y^{\prime }&=-F \left (x \right ) \left (y^{2}-2 y x -x^{2}\right )+\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.599 |
|
| 15743 |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{t} {\mathrm e}^{i t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.600 |
|
| 15744 |
\begin{align*}
x^{3} {\mathrm e}^{2 x^{2}+3 y^{2}}-y^{3} {\mathrm e}^{-x^{2}-2 y^{2}} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.601 |
|
| 15745 |
\begin{align*}
\left (x -y\right ) \sqrt {y^{\prime }}&=a \left (1+y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.602 |
|
| 15746 |
\begin{align*}
2 x^{\prime \prime }-5 x^{\prime }-3 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.602 |
|
| 15747 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=12 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.602 |
|
| 15748 |
\begin{align*}
x^{2} y^{\prime }-y x&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.604 |
|
| 15749 |
\begin{align*}
y^{\prime }&=\frac {1+2 y}{x \left (-2+x y^{2}+2 x y^{3}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.605 |
|
| 15750 |
\begin{align*}
x +y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.605 |
|
| 15751 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-30 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.606 |
|
| 15752 |
\begin{align*}
x^{\prime }+\frac {\left (1+t \right ) x}{2 t}&=\frac {1+t}{t x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.607 |
|
| 15753 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=4 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.608 |
|
| 15754 |
\begin{align*}
3 x^{3} y^{2} y^{\prime }-x^{2} y^{3}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.608 |
|
| 15755 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }-7 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.608 |
|
| 15756 |
\begin{align*}
L i^{\prime }+R i&=E \sin \left (2 t \right ) \\
i \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.609 |
|
| 15757 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}-2 y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.609 |
|
| 15758 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.609 |
|
| 15759 |
\begin{align*}
y^{\prime } x +x +\tan \left (x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.610 |
|
| 15760 |
\begin{align*}
y^{\prime }+f \left (x \right ) y^{2}+g \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.610 |
|
| 15761 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.610 |
|
| 15762 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }-\left (x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
3.610 |
|
| 15763 |
\begin{align*}
y^{\prime \prime }+36 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.611 |
|
| 15764 |
\begin{align*}
y^{\prime }&=\frac {2 y}{1+t} \\
y \left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.612 |
|
| 15765 |
\begin{align*}
y^{\prime } t&=-y+t^{3} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.612 |
|
| 15766 |
\begin{align*}
y^{\prime }&=\frac {\sec \left (y\right )^{2}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.612 |
|
| 15767 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (-2\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.612 |
|
| 15768 |
\begin{align*}
y+y^{\prime }&=4+3 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.612 |
|
| 15769 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.613 |
|
| 15770 |
\begin{align*}
t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.613 |
|
| 15771 |
\begin{align*}
y^{\prime }-y^{2}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.613 |
|
| 15772 |
\begin{align*}
3 y^{\prime } x&=3 x^{{2}/{3}}+\left (1-3 y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.614 |
|
| 15773 |
\begin{align*}
x^{3} \left (1+y^{2}\right ) y^{\prime }+3 x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.614 |
|
| 15774 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+4 y x&=x \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.614 |
|
| 15775 |
\begin{align*}
y^{\prime \prime }&=4 \sin \left (x \right )-4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.615 |
|
| 15776 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (a \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.615 |
|
| 15777 |
\begin{align*}
y^{\prime } t&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.615 |
|
| 15778 |
\begin{align*}
1+y \tan \left (y x \right )+x \tan \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.615 |
|
| 15779 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.616 |
|
| 15780 |
\begin{align*}
t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.617 |
|
| 15781 |
\begin{align*}
y^{\prime }&=-F \left (x \right ) \left (x^{2}+2 y x -y^{2}\right )+\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.617 |
|
| 15782 |
\begin{align*}
y^{2}+\left (-y+{\mathrm e}^{x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.618 |
|
| 15783 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=8 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.618 |
|
| 15784 |
\begin{align*}
y^{\prime }&=x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.618 |
|
| 15785 |
\begin{align*}
y^{\prime } t&=y+t^{3} \\
y \left (1\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.620 |
|
| 15786 |
\begin{align*}
a x y^{\prime }+2 y&=y y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.620 |
|
| 15787 |
\begin{align*}
y^{\prime \prime }-8 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.620 |
|
| 15788 |
\begin{align*}
\frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.621 |
|
| 15789 |
\begin{align*}
y^{\prime } x -y-x^{2} \sin \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.621 |
|
| 15790 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=4+{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.621 |
|
| 15791 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=-6 x^{3}+4 x^{2} \\
y \left (2\right ) &= 4 \\
y^{\prime }\left (2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.622 |
|
| 15792 |
\begin{align*}
x^{2} {\mathrm e}^{y+x^{2}} \left (2 x^{2}+3\right )+4 x +\left (x^{3} {\mathrm e}^{y+x^{2}}-12 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.623 |
|
| 15793 |
\begin{align*}
\cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=2 x \cos \left (x \right )^{2} \\
y \left (\frac {\pi }{4}\right ) &= -\frac {15 \sqrt {2}\, \pi ^{2}}{32} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.623 |
|
| 15794 |
\begin{align*}
y^{\prime }&=-\frac {2 \arctan \left (y\right )}{1+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.625 |
|
| 15795 |
\begin{align*}
\left (x^{3}+x \right ) y^{\prime }+y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.625 |
|
| 15796 |
\begin{align*}
a {y^{\prime }}^{2}+b y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.625 |
|
| 15797 |
\begin{align*}
y^{\prime }&=\frac {-3 x^{2} y+F \left (x^{3} y\right )}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.626 |
|
| 15798 |
\begin{align*}
y^{\prime }-\frac {2 x y}{x^{2}+1}&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.627 |
|
| 15799 |
\begin{align*}
\left (a +x \right ) y+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.627 |
|
| 15800 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.628 |
|