| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 18801 |
\begin{align*}
x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.497 |
|
| 18802 |
\begin{align*}
2 x \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=4 x^{2}+\sin \left (y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.498 |
|
| 18803 |
\begin{align*}
\cot \left (x \right ) y^{\prime }+y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.498 |
|
| 18804 |
\begin{align*}
y^{\prime \prime }&=a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.498 |
|
| 18805 |
\begin{align*}
5 y y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.500 |
|
| 18806 |
\begin{align*}
y^{\prime }-y&=y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.500 |
|
| 18807 |
\begin{align*}
y^{\prime \prime }&=y^{\prime } \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.500 |
|
| 18808 |
\begin{align*}
y^{\prime }&=\frac {\cot \left (t \right ) y}{1+y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.503 |
|
| 18809 |
\begin{align*}
4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.503 |
|
| 18810 |
\begin{align*}
2 x^{2} y^{\prime \prime }-7 x y^{\prime }+7 y&=0 \\
y \left (1\right ) &= -1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.503 |
|
| 18811 |
\begin{align*}
\left (1+\cos \left (\theta \right )\right ) r^{\prime }&=-r \sin \left (\theta \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.503 |
|
| 18812 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.504 |
|
| 18813 |
\begin{align*}
y&=2 x y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.504 |
|
| 18814 |
\begin{align*}
y^{\prime }&=\sec \left (x \right )^{2}+y \sec \left (x \right ) \operatorname {Csx} \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.506 |
|
| 18815 |
\begin{align*}
y^{\prime }+y \cot \left (x \right )&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.507 |
|
| 18816 |
\begin{align*}
y^{3}+y+1+x \left (x -3 y^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.507 |
|
| 18817 |
\begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{\sqrt {y}+F \left (\frac {x -y}{\sqrt {y}}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.508 |
|
| 18818 |
\begin{align*}
x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.509 |
|
| 18819 |
\begin{align*}
b y+2 x^{2} \left (x +a \right ) y^{\prime }+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.509 |
|
| 18820 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.509 |
|
| 18821 |
\begin{align*}
y^{\prime }&=x^{3}-2 y x \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.509 |
|
| 18822 |
\begin{align*}
1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.510 |
|
| 18823 |
\begin{align*}
\left (x -1\right ) y^{\prime }-3 y&=\left (x -1\right )^{5} \\
y \left (-1\right ) &= 16 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.510 |
|
| 18824 |
\begin{align*}
y^{\prime \prime }&=x {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.511 |
|
| 18825 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.514 |
|
| 18826 |
\begin{align*}
y t +\left (t^{2}+1\right ) y^{\prime }&=\left (t^{2}+1\right )^{{5}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.517 |
|
| 18827 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
3.517 |
|
| 18828 |
\begin{align*}
1+3 x^{2} y^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.517 |
|
| 18829 |
\begin{align*}
x_{1}^{\prime }&=x_{2}+f_{1} \left (t \right ) \\
x_{2}^{\prime }&=-x_{1}+f_{2} \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.520 |
|
| 18830 |
\begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.520 |
|
| 18831 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}-\ln \left (y\right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.521 |
|
| 18832 |
\begin{align*}
x^{\prime }+5 x&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.521 |
|
| 18833 |
\begin{align*}
y^{\prime }&=-a n \,x^{n -1} y^{2}+c \,x^{m} \left (a \,x^{n}+b \right ) y-c \,x^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.522 |
|
| 18834 |
\begin{align*}
x y^{\prime \prime }+\left (a \,x^{3}+b \right ) y^{\prime }+a \left (b -1\right ) x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.522 |
|
| 18835 |
\begin{align*}
x \left (-a^{2}+x^{2}+y^{2}\right )+y \left (x^{2}-y^{2}-b^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.523 |
|
| 18836 |
\begin{align*}
y^{\prime }&=1+x^{2}+y^{2}+x^{2} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.524 |
|
| 18837 |
\begin{align*}
y^{\prime }&=t^{2}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.524 |
|
| 18838 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=x^{2} y \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.525 |
|
| 18839 |
\begin{align*}
x y^{\prime }+y&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.525 |
|
| 18840 |
\begin{align*}
y^{\prime }&={\mathrm e}^{3 x -2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.526 |
|
| 18841 |
\begin{align*}
y^{2} \left (x^{2}+2\right )+\left (x^{3}+y^{3}\right ) \left (-x y^{\prime }+y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.527 |
|
| 18842 |
\begin{align*}
x y^{\prime \prime }-5 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.527 |
|
| 18843 |
\begin{align*}
y^{\prime }&=2 y x +3 x^{2} {\mathrm e}^{x^{2}} \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.528 |
|
| 18844 |
\begin{align*}
x^{2}+y^{2}-x^{2} y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.528 |
|
| 18845 |
\begin{align*}
\left (a \left (a +1\right )+b^{2} x^{2}\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.529 |
|
| 18846 |
\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*} |
✓ |
✓ |
✓ |
✓ |
3.529 |
|
| 18847 |
\begin{align*}
y^{\prime }&=8 x^{3} {\mathrm e}^{-2 y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.530 |
|
| 18848 |
\begin{align*}
{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.531 |
|
| 18849 |
\begin{align*}
y \left (2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+3 f \left (x \right ) y^{\prime }+y^{\prime \prime }&=2 y^{3} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3.532 |
|
| 18850 |
\begin{align*}
{y^{\prime }}^{3}-a x y^{\prime }+x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.532 |
|
| 18851 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=5 \operatorname {Heaviside}\left (-3+t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.534 |
|
| 18852 |
\begin{align*}
y^{2}+\left (y x +y^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.534 |
|
| 18853 |
\begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.534 |
|
| 18854 |
\begin{align*}
3 y^{\prime }+\frac {2 y}{x +1}&=\frac {x^{3}}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.534 |
|
| 18855 |
\begin{align*}
x^{2} {\mathrm e}^{x^{2}+y} \left (2 x^{2}+3\right )+4 x +\left (x^{3} {\mathrm e}^{x^{2}+y}-12 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.535 |
|
| 18856 |
\begin{align*}
y^{\prime }-\frac {y-x f \left (x^{2}+a y^{2}\right )}{x +a y f \left (x^{2}+a y^{2}\right )}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.535 |
|
| 18857 |
\begin{align*}
3-2 y x -\left (x^{2}+\frac {1}{y^{2}}+\frac {1}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.537 |
|
| 18858 |
\begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (L \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.538 |
|
| 18859 |
\begin{align*}
y^{\prime \prime }&=\sqrt {y^{\prime }+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.538 |
|
| 18860 |
\begin{align*}
y^{\prime \prime }&=g \left (x \right )+f \left (x \right ) y^{2}+\left (f \left (x \right )-2 y\right ) y^{\prime } \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3.539 |
|
| 18861 |
\begin{align*}
\frac {y^{\prime }}{2}&=\sqrt {y+1}\, \cos \left (x \right ) \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.539 |
|
| 18862 |
\begin{align*}
2 y+t y^{\prime }&=\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.539 |
|
| 18863 |
\begin{align*}
y^{\prime } \ln \left (x -y\right )&=1+\ln \left (x -y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.539 |
|
| 18864 |
\begin{align*}
y^{\prime }&=t \left (3-y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.540 |
|
| 18865 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y&=\left (x +1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.540 |
|
| 18866 |
\begin{align*}
x^{2} \left (-x^{2}+1\right ) y^{\prime }&=\left (x -3 x^{3} y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.541 |
|
| 18867 |
\begin{align*}
x^{{10}/{3}}-2 y+x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.542 |
|
| 18868 |
\begin{align*}
y^{\prime }-5 y&={\mathrm e}^{x} x^{2}-x \,{\mathrm e}^{5 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.542 |
|
| 18869 |
\begin{align*}
y^{\prime }+3 y&=5 \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.543 |
|
| 18870 |
\begin{align*}
\left (y^{2}+4 \sin \left (x \right )\right ) y^{\prime }-\cos \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.544 |
|
| 18871 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=f \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.544 |
|
| 18872 |
\begin{align*}
y^{2}+\left (y x +y^{2}-1\right ) y^{\prime }&=0 \\
y \left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.545 |
|
| 18873 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.546 |
|
| 18874 |
\begin{align*}
\left (x +a \right ) y^{\prime }&=b x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.546 |
|
| 18875 |
\begin{align*}
x y^{\prime }-y&=x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.546 |
|
| 18876 |
\begin{align*}
2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.546 |
|
| 18877 |
\begin{align*}
\left (y+a \right ) y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.548 |
|
| 18878 |
\begin{align*}
y y^{\prime }&=x -1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.549 |
|
| 18879 |
\begin{align*}
y^{\prime }&=\frac {x \left (1+x^{2}+y^{2}\right )}{-y^{3}-x^{2} y-y+y^{6}+3 x^{2} y^{4}+3 y^{2} x^{4}+x^{6}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.549 |
|
| 18880 |
\begin{align*}
x^{\prime \prime }+4 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.549 |
|
| 18881 |
\begin{align*}
Q^{\prime \prime }+k Q&=e \left (t \right ) \\
Q \left (0\right ) &= q_{0} \\
Q^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.549 |
|
| 18882 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+y^{2}-2 y x +1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.549 |
|
| 18883 |
\begin{align*}
-\left (-2 x^{2}+3\right ) y+4 x^{3} y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.550 |
|
| 18884 |
\begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }+x y^{\prime }+\left (4 x^{3}-4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.550 |
|
| 18885 |
\begin{align*}
\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime }&=-x +2 y x -{\mathrm e}^{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.552 |
|
| 18886 |
\begin{align*}
-5 y-3 x y^{\prime }+x^{2} y^{\prime \prime }&=x^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.553 |
|
| 18887 |
\begin{align*}
3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.553 |
|
| 18888 |
\begin{align*}
{y^{\prime }}^{2}-4 y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.553 |
|
| 18889 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=x^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.554 |
|
| 18890 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=2 \,{\mathrm e}^{-y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.554 |
|
| 18891 |
\begin{align*}
2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.556 |
|
| 18892 |
\begin{align*}
-y+2 x y^{\prime }+x^{2} \ln \left (x \right ) y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=2 x^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.556 |
|
| 18893 |
\begin{align*}
y^{\prime }&={\mathrm e}^{2 y+10 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.556 |
|
| 18894 |
\begin{align*}
y^{\prime }+2 y x&=y^{2} {\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.556 |
|
| 18895 |
\begin{align*}
y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.558 |
|
| 18896 |
\begin{align*}
y^{\prime }&=1+x \left (-x^{3}+2\right )+\left (2 x^{2}-y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.560 |
|
| 18897 |
\begin{align*}
\left (2 x y^{3}+y x +x^{2}\right ) y^{\prime }-y x +y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.560 |
|
| 18898 |
\begin{align*}
\left (x^{2}+x -2\right ) y^{\prime }+3 \left (x +1\right ) y&=x -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.560 |
|
| 18899 |
\begin{align*}
t y^{\prime }&=-y+t^{3} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.561 |
|
| 18900 |
\begin{align*}
x y^{\prime }+a y^{2}-b y+c \,x^{2 b}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.563 |
|