| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15801 |
\begin{align*}
2 x y^{2}+3 x^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.066 |
|
| 15802 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=\sin \left (b x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.068 |
|
| 15803 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&=-3 t -4 \,{\mathrm e}^{2 t} t^{2} \\
y \left (0\right ) &= -{\frac {7}{2}} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.068 |
|
| 15804 |
\begin{align*}
y^{\prime }&=10+{\mathrm e}^{x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.069 |
|
| 15805 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.069 |
|
| 15806 |
\begin{align*}
y^{\prime }-3 y&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.070 |
|
| 15807 |
\begin{align*}
x y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (c -1\right ) \left (a x +b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.071 |
|
| 15808 |
\begin{align*}
x^{3}+3 y-x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.072 |
|
| 15809 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (-\nu ^{2}+x^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.072 |
|
| 15810 |
\begin{align*}
x^{\prime }+2 x&=6 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.072 |
|
| 15811 |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.072 |
|
| 15812 |
\begin{align*}
10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.073 |
|
| 15813 |
\begin{align*}
y^{\prime }&=\tan \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.073 |
|
| 15814 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.073 |
|
| 15815 |
\begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.073 |
|
| 15816 |
\begin{align*}
x^{\prime }&=-\frac {x}{2}+2 y-3 z \\
y^{\prime }&=y-\frac {z}{2} \\
z^{\prime }&=-2 x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.075 |
|
| 15817 |
\begin{align*}
3 y^{\prime \prime }-y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.075 |
|
| 15818 |
\begin{align*}
5 {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.076 |
|
| 15819 |
\begin{align*}
b y+2 x^{2} \left (x +a \right ) y^{\prime }+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.076 |
|
| 15820 |
\begin{align*}
x^{2} y^{\prime \prime }+5 x y^{\prime }+29 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.076 |
|
| 15821 |
\begin{align*}
2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.076 |
|
| 15822 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
2.076 |
|
| 15823 |
\begin{align*}
2 x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.077 |
|
| 15824 |
\begin{align*}
y^{\prime }&=\cos \left ({\mathrm e}^{y x}\right ) \\
y \left (0\right ) &= -4 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.077 |
|
| 15825 |
\begin{align*}
x^{\prime }&=x+x^{2} {\mathrm e}^{\theta } \\
x \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.078 |
|
| 15826 |
\begin{align*}
y^{\prime }&=4 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.078 |
|
| 15827 |
\begin{align*}
y^{\prime }+a y&=Q \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.079 |
|
| 15828 |
\begin{align*}
y^{\prime }&=-\ln \left (y\right ) y \\
y \left (0\right ) &= {\mathrm e} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.079 |
|
| 15829 |
\begin{align*}
y^{\prime }&=\left \{\begin {array}{cc} 0 & t =0 \\ \sin \left (\frac {1}{t}\right ) & \operatorname {otherwise} \end {array}\right . \\
\end{align*}
Using Laplace transform method. |
✓ |
✗ |
✓ |
✓ |
2.079 |
|
| 15830 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & t <6 \\ 1 & 6\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.080 |
|
| 15831 |
\begin{align*}
y^{\prime }-1&={\mathrm e}^{x +2 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.080 |
|
| 15832 |
\begin{align*}
y^{\prime }+\alpha y&={\mathrm e}^{\beta x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.081 |
|
| 15833 |
\begin{align*}
y^{\prime }-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.081 |
|
| 15834 |
\begin{align*}
y^{\prime }&=2 y+\delta \left (-3+t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.081 |
|
| 15835 |
\begin{align*}
2 y+2 \left (2-x \right ) y^{\prime }+\left (2-x \right )^{2} x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.082 |
|
| 15836 |
\begin{align*}
y^{\prime \prime }+16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.082 |
|
| 15837 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.082 |
|
| 15838 |
\begin{align*}
y^{\prime }&=\frac {x \left (x^{2}+1\right )}{4 y^{3}} \\
y \left (0\right ) &= -\frac {\sqrt {2}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.083 |
|
| 15839 |
\begin{align*}
p^{\prime }&=p-p^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.083 |
|
| 15840 |
\begin{align*}
2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (5 x^{2}+3 x +3\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.084 |
|
| 15841 |
\begin{align*}
x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.084 |
|
| 15842 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.084 |
|
| 15843 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.085 |
|
| 15844 |
\begin{align*}
y^{\prime }-5 y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.085 |
|
| 15845 |
\begin{align*}
\left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= a \\
y^{\prime }\left (0\right ) &= b \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.085 |
|
| 15846 |
\begin{align*}
x^{3}+\frac {y}{x}+\left (y^{2}+\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.086 |
|
| 15847 |
\begin{align*}
2 y+2 \left (1-x \right ) y^{\prime }+\left (2-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.086 |
|
| 15848 |
\begin{align*}
x \left (x +1\right )^{2} y y^{\prime \prime }-x \left (x +1\right )^{2} {y^{\prime }}^{2}+2 \left (x +1\right )^{2} y y^{\prime }-a \left (x +2\right ) y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.086 |
|
| 15849 |
\begin{align*}
y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.086 |
|
| 15850 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{\left (x^{3}+1\right ) y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.087 |
|
| 15851 |
\begin{align*}
6 y-2 x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.087 |
|
| 15852 |
\begin{align*}
x^{\prime }&=3 x \left (5-x\right ) \\
x \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| 15853 |
\begin{align*}
y^{\prime }+7 y&={\mathrm e}^{3 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| 15854 |
\begin{align*}
3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| 15855 |
\begin{align*}
x^{\prime }&=2 \\
x \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| 15856 |
\begin{align*}
b y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.089 |
|
| 15857 |
\begin{align*}
y y^{\prime }&=x +y^{2}-y^{2} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.089 |
|
| 15858 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-16 y&=8 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.089 |
|
| 15859 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.089 |
|
| 15860 |
\begin{align*}
y^{\prime }+\frac {y}{3}&=\frac {\left (1-2 x \right ) y^{4}}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.089 |
|
| 15861 |
\begin{align*}
y^{\prime \prime }+2 x y^{\prime }+y&=4 x y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.089 |
|
| 15862 |
\begin{align*}
y^{\prime }-\frac {3 y}{x}&=2 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.089 |
|
| 15863 |
\begin{align*}
y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} x^{2}-{y^{\prime }}^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.091 |
|
| 15864 |
\begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+2 y&={\mathrm e}^{2 x} \left (x^{4}+x +24\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.092 |
|
| 15865 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }+y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.092 |
|
| 15866 |
\begin{align*}
y^{2} y^{\prime }&=2+3 y^{6} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.092 |
|
| 15867 |
\begin{align*}
x^{2} \left (1+{y^{\prime }}^{2}\right )^{3}-a^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.093 |
|
| 15868 |
\begin{align*}
y^{\prime \prime }&=4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.093 |
|
| 15869 |
\begin{align*}
x y^{\prime }+2 y&=\frac {2}{x^{2}}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.094 |
|
| 15870 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.094 |
|
| 15871 |
\begin{align*}
x^{2}+y^{2}+x -\left (2 x^{2}+2 y^{2}-y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.094 |
|
| 15872 |
\begin{align*}
3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.094 |
|
| 15873 |
\begin{align*}
y^{\prime \prime }-f \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.096 |
|
| 15874 |
\begin{align*}
t^{2} y^{\prime \prime }+7 t y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.096 |
|
| 15875 |
\begin{align*}
y-\left (x +3\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.097 |
|
| 15876 |
\begin{align*}
y^{\prime }-y x&=-x^{5}+4 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.097 |
|
| 15877 |
\begin{align*}
-\left (x +1\right ) y+x \left (3-5 x \right ) y^{\prime }+2 x^{2} \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.098 |
|
| 15878 |
\begin{align*}
2 y^{\prime }+x y^{\prime \prime }&=a \,x^{2 k} {y^{\prime }}^{k} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.099 |
|
| 15879 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.099 |
|
| 15880 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&=-5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \\
y \left (0\right ) &= -4 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.099 |
|
| 15881 |
\begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= {\frac {1}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.099 |
|
| 15882 |
\begin{align*}
\sqrt {x}\, y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.099 |
|
| 15883 |
\begin{align*}
2 y+y^{\prime }&=x^{2}+2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.099 |
|
| 15884 |
\begin{align*}
x^{2}+a_{1} x y+a_{2} y^{2}+\left (x^{2}+b_{1} x y+b_{2} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.100 |
|
| 15885 |
\begin{align*}
\frac {1}{x}+y+\left (x +3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.100 |
|
| 15886 |
\begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y \left (L \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.101 |
|
| 15887 |
\begin{align*}
\sin \left (\pi \,x^{2}\right ) y^{\prime \prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.102 |
|
| 15888 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.103 |
|
| 15889 |
\begin{align*}
x^{2} y^{2} y^{\prime \prime }-3 x y^{2} y^{\prime }+4 y^{3}+x^{6}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.103 |
|
| 15890 |
\begin{align*}
y^{\prime }&=2 x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.103 |
|
| 15891 |
\begin{align*}
\frac {x+y \,{\mathrm e}^{y}}{x^{\prime }}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.104 |
|
| 15892 |
\begin{align*}
{y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.105 |
|
| 15893 |
\begin{align*}
\left (x^{2}-y^{4}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.105 |
|
| 15894 |
\begin{align*}
3 x^{2} y^{2}+\left (2 x^{3} y+x^{3} y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.105 |
|
| 15895 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\operatorname {Heaviside}\left (-3+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.105 |
|
| 15896 |
\begin{align*}
y^{\prime }&=y+{\mathrm e}^{y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
2.105 |
|
| 15897 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.106 |
|
| 15898 |
\begin{align*}
\left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.108 |
|
| 15899 |
\begin{align*}
y^{\prime }&=y+\frac {1}{1-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.108 |
|
| 15900 |
\begin{align*}
y^{\prime \prime }+y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.108 |
|