| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 19801 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{-2 y} \sin \left (x \right )}{x^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.175 |
|
| 19802 |
\begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.175 |
|
| 19803 |
\begin{align*}
\frac {c y^{\prime \prime }}{\omega ^{2}}+c y&=\cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.176 |
|
| 19804 |
\begin{align*}
\left (x -6 y\right )^{2} y^{\prime }+a +2 y x -6 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.177 |
|
| 19805 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.177 |
|
| 19806 |
\begin{align*}
y y^{\prime }+b y^{2}&=a \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.178 |
|
| 19807 |
\begin{align*}
\cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.178 |
|
| 19808 |
\begin{align*}
\left (x +1\right )^{3} y^{\prime \prime }+3 \left (x +1\right )^{2} y^{\prime }+\left (x +1\right ) y&=6 \ln \left (x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.179 |
|
| 19809 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\
y \left (\pi \right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 2 \,{\mathrm e}^{-\pi }-2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.181 |
|
| 19810 |
\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*} |
✗ |
✓ |
✓ |
✗ |
4.181 |
|
| 19811 |
\begin{align*}
y^{\prime }+\frac {x y}{-x^{2}+1}&=x \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.182 |
|
| 19812 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.182 |
|
| 19813 |
\begin{align*}
b \sin \left (y\right )+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.183 |
|
| 19814 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y&=4 \,{\mathrm e}^{x} \\
y \left (-\infty \right ) &= 0 \\
y^{\prime }\left (-1\right ) &= -{\mathrm e}^{-1} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
4.184 |
|
| 19815 |
\begin{align*}
2 y y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.184 |
|
| 19816 |
\begin{align*}
y^{\prime }&=y \,{\mathrm e}^{x +y} \left (x^{2}+1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.185 |
|
| 19817 |
\begin{align*}
r^{\prime } \left (1+\frac {\cos \left (\theta \right )}{2}\right )-r \sin \left (\theta \right )&=0 \\
r \left (\frac {\pi }{2}\right ) &= 2 a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.185 |
|
| 19818 |
\begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.185 |
|
| 19819 |
\begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.186 |
|
| 19820 |
\begin{align*}
\left (-x^{2}+x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y-a \,x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.187 |
|
| 19821 |
\begin{align*}
y^{\prime }&=x \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.187 |
|
| 19822 |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{y} \\
y \left (1\right ) &= {\frac {5}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.189 |
|
| 19823 |
\begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.189 |
|
| 19824 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.190 |
|
| 19825 |
\begin{align*}
\left (x +y^{2}\right ) y^{\prime }+y&=b x +a \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.191 |
|
| 19826 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=2 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.191 |
|
| 19827 |
\begin{align*}
6 x +y^{2}+\left (2 y x -3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.191 |
|
| 19828 |
\begin{align*}
x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.192 |
|
| 19829 |
\begin{align*}
w^{\prime }&=\left (w^{2}-2\right ) \arctan \left (w\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.194 |
|
| 19830 |
\begin{align*}
\left (x^{2}+y^{2}+x \right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.198 |
|
| 19831 |
\begin{align*}
y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
4.198 |
|
| 19832 |
\begin{align*}
y y^{\prime \prime }&=y^{2} \left (f \left (x \right ) y+g^{\prime }\left (x \right )\right )+y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
4.201 |
|
| 19833 |
\begin{align*}
3 y^{2} y^{\prime }&=2 x -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.202 |
|
| 19834 |
\begin{align*}
\cos \left (y\right )&=x y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.202 |
|
| 19835 |
\begin{align*}
3 x^{2}+3 x y^{2}+\left (3 x^{2} y-3 y^{2}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.202 |
|
| 19836 |
\begin{align*}
x^{\prime }+2 x&=t^{2}+4 t +7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.203 |
|
| 19837 |
\begin{align*}
x y^{\prime }+y+x y \left (y^{\prime }+1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.203 |
|
| 19838 |
\begin{align*}
\left (y^{2} a^{2}-b^{2}\right ) {y^{\prime \prime }}^{2}-2 a^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2} {y^{\prime }}^{2}-1\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.204 |
|
| 19839 |
\begin{align*}
y^{\prime }&=3 y \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.204 |
|
| 19840 |
\begin{align*}
x^{2} \left (y^{\prime }+a y^{2}\right )-b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.205 |
|
| 19841 |
\begin{align*}
3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.206 |
|
| 19842 |
\begin{align*}
\cot \left (x \right ) y^{\prime }+y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.207 |
|
| 19843 |
\begin{align*}
p^{\prime }+2 t p&=p+4 t -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.207 |
|
| 19844 |
\begin{align*}
x y^{\prime }-y \left (\ln \left (y x \right )-1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.207 |
|
| 19845 |
\begin{align*}
\left (y^{2}-x \right ) y^{\prime }-y+x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.207 |
|
| 19846 |
\begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }-y&=\sqrt {t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.207 |
|
| 19847 |
\begin{align*}
2 y-6 x +\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.208 |
|
| 19848 |
\begin{align*}
y^{\prime }&=\frac {x +y+y^{2}-2 x y \ln \left (x \right )+x^{2} \ln \left (x \right )^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.209 |
|
| 19849 |
\begin{align*}
4 x y^{\prime \prime }+2 y^{\prime }+y&=1 \\
y \left (\infty \right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.209 |
|
| 19850 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=\operatorname {Heaviside}\left (t -1\right )+\delta \left (t -2\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.213 |
|
| 19851 |
\begin{align*}
y {y^{\prime }}^{2}+2 y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.214 |
|
| 19852 |
\begin{align*}
-\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.214 |
|
| 19853 |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right )&=x \,{\mathrm e}^{x} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
4.214 |
|
| 19854 |
\begin{align*}
\cos \left (x \right )+\ln \left (y\right )+\left (\frac {x}{y}+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.216 |
|
| 19855 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.217 |
|
| 19856 |
\begin{align*}
\left (t +1\right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= -9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.217 |
|
| 19857 |
\begin{align*}
y y^{\prime \prime }+1&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.218 |
|
| 19858 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.218 |
|
| 19859 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
4.220 |
|
| 19860 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+2&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.220 |
|
| 19861 |
\begin{align*}
y^{\prime \prime }+9 y&=18 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.223 |
|
| 19862 |
\begin{align*}
x y^{\prime }&=x^{2} \sin \left (x \right )+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.224 |
|
| 19863 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+x^{2}-y \,\operatorname {arccot}\left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.224 |
|
| 19864 |
\begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.225 |
|
| 19865 |
\begin{align*}
x +y y^{\prime }+\frac {x y^{\prime }-y}{x^{2}+y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.227 |
|
| 19866 |
\begin{align*}
t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
4.229 |
|
| 19867 |
\begin{align*}
x \ln \left (x \right ) y^{\prime }-y&=3 x^{3} \ln \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.230 |
|
| 19868 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.233 |
|
| 19869 |
\begin{align*}
x^{2} y^{\prime }&=x^{2} y^{2}-a^{2} x^{4}+a \left (1-2 b \right ) x^{2}-b \left (b +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.235 |
|
| 19870 |
\begin{align*}
\sin \left (x \right )+y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.238 |
|
| 19871 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }-\frac {4 y}{x}&=x^{3}+x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.238 |
|
| 19872 |
\begin{align*}
{\mathrm e}^{x} \left (y^{2} x^{4}+4 x^{3} y^{2}+1\right )+\left (2 x^{4} y \,{\mathrm e}^{x}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.239 |
|
| 19873 |
\begin{align*}
2 y x +y^{4}+\left (x y^{3}-2 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.240 |
|
| 19874 |
\begin{align*}
x^{\prime }+2 x t&={\mathrm e}^{-t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.240 |
|
| 19875 |
\begin{align*}
\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.240 |
|
| 19876 |
\begin{align*}
y^{\prime }+\tan \left (x \right ) \cot \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.243 |
|
| 19877 |
\begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.243 |
|
| 19878 |
\begin{align*}
a \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.244 |
|
| 19879 |
\begin{align*}
y \sin \left (x \right )+\cos \left (x \right )^{2}-\cos \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.245 |
|
| 19880 |
\begin{align*}
y^{2} y^{\prime }+x \left (2-y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.247 |
|
| 19881 |
\begin{align*}
y^{\prime \prime }-\left (8 \,{\mathrm e}^{2 x}+2\right ) y^{\prime }+4 \,{\mathrm e}^{4 x} y&={\mathrm e}^{6 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.248 |
|
| 19882 |
\begin{align*}
{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.249 |
|
| 19883 |
\begin{align*}
x y^{\prime }-2 y&=x^{3} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.251 |
|
| 19884 |
\begin{align*}
y^{\prime }&=\frac {x \left (-x -1+x^{2}-2 x^{2} y+2 x^{4}\right )}{\left (x^{2}-y\right ) \left (x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.252 |
|
| 19885 |
\begin{align*}
4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.252 |
|
| 19886 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2} y^{3}+y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.252 |
|
| 19887 |
\begin{align*}
y&=y^{\prime } x \left (y^{\prime }+1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.254 |
|
| 19888 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=8 \,{\mathrm e}^{x}+9 \\
y \left (-\infty \right ) &= 3 \\
\end{align*} |
✗ |
✓ |
✗ |
✓ |
4.254 |
|
| 19889 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.256 |
|
| 19890 |
\begin{align*}
4 y x -6+x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.256 |
|
| 19891 |
\begin{align*}
\left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
4.256 |
|
| 19892 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}+y^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
4.256 |
|
| 19893 |
\begin{align*}
4 x^{2} y^{\prime \prime }-\left (-4 k x +4 m^{2}+x^{2}-1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.257 |
|
| 19894 |
\begin{align*}
y^{\prime }&=\frac {\sin \left (x \right )}{\cos \left (y\right )+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
4.257 |
|
| 19895 |
\begin{align*}
y^{4} y^{\prime }&=t +2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.258 |
|
| 19896 |
\begin{align*}
1+y^{2}&=\left (x^{2}+x \right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.259 |
|
| 19897 |
\begin{align*}
x^{3}+x y^{2}-y+\left (x^{2} y+y^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.259 |
|
| 19898 |
\begin{align*}
y^{3}-25 y+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.260 |
|
| 19899 |
\begin{align*}
y^{\prime }&=\sin \left (x -y+1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.260 |
|
| 19900 |
\begin{align*}
y^{\prime }&=y \cot \left (x \right )+\csc \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.261 |
|