| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 23101 |
\begin{align*}
6 x y^{2} y^{\prime }+x +2 y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.723 |
|
| 23102 |
\begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.723 |
|
| 23103 |
\begin{align*}
\cos \left (x \right ) \cos \left (y\right )+2 x -\left (\sin \left (x \right ) \sin \left (y\right )+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.727 |
|
| 23104 |
\begin{align*}
x \left (-y x +1\right )^{2} y^{\prime }+\left (1+x^{2} y^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.730 |
|
| 23105 |
\begin{align*}
\left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.734 |
|
| 23106 |
\begin{align*}
x \ln \left (y\right )+y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.735 |
|
| 23107 |
\begin{align*}
x y^{\prime }-1+y&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.740 |
|
| 23108 |
\begin{align*}
x \cos \left (y\right ) y^{\prime }-\sin \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.744 |
|
| 23109 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (x \right ) \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.744 |
|
| 23110 |
\begin{align*}
x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.747 |
|
| 23111 |
\begin{align*}
y^{\prime }&=-\frac {y \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}+y \ln \left (x \right ) x^{2}+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.748 |
|
| 23112 |
\begin{align*}
\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.751 |
|
| 23113 |
\begin{align*}
y^{\prime }&=\frac {y+2}{x +1}+\tan \left (\frac {y-2 x}{x +1}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.752 |
|
| 23114 |
\begin{align*}
x^{\prime }&=3 x-7 y+4 \sin \left (t \right )+\left (-4+t \right ) {\mathrm e}^{4 t} \\
y^{\prime }&=x+y+8 \sin \left (t \right )+\left (2 t +1\right ) {\mathrm e}^{4 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.753 |
|
| 23115 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.756 |
|
| 23116 |
\begin{align*}
x y^{\prime }&=a \,x^{2 n} \ln \left (x \right ) y^{2}+\left (b \,x^{n} \ln \left (x \right )-n \right ) y+c \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.761 |
|
| 23117 |
\begin{align*}
x -y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.762 |
|
| 23118 |
\begin{align*}
x y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.762 |
|
| 23119 |
\begin{align*}
y+\left (x +x^{3} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.766 |
|
| 23120 |
\begin{align*}
x^{4} y^{\prime }+a^{2}+y^{2} x^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.767 |
|
| 23121 |
\begin{align*}
\left (-x +a \right ) y^{\prime }&=y+\left (c x +b \right ) y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.770 |
|
| 23122 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\
y \left (0\right ) &= -{\frac {5}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.770 |
|
| 23123 |
\begin{align*}
\ln \left (y\right ) y-x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.771 |
|
| 23124 |
\begin{align*}
\sin \left (\ln \left (x \right )\right )-\cos \left (\ln \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.773 |
|
| 23125 |
\begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.774 |
|
| 23126 |
\begin{align*}
x y^{\prime }&=y \left (1+2 y x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.776 |
|
| 23127 |
\begin{align*}
x y^{\prime }&=y f \left (x^{m} y^{n}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.776 |
|
| 23128 |
\begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.779 |
|
| 23129 |
\begin{align*}
x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x +\left (x^{3}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.779 |
|
| 23130 |
\begin{align*}
2 y y^{\prime \prime }&=4 y^{2}+8 y^{3}+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.780 |
|
| 23131 |
\begin{align*}
2 \cos \left (x \right ) y+3 \sin \left (x \right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.782 |
|
| 23132 |
\begin{align*}
\left (4 k x -4 p^{2}-x^{2}+1\right ) y+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.783 |
|
| 23133 |
\begin{align*}
x \left (y^{2}+x^{2}-a \right ) y^{\prime }-\left (a +x^{2}+y^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.792 |
|
| 23134 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.792 |
|
| 23135 |
\begin{align*}
x y^{\prime }+y&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.793 |
|
| 23136 |
\begin{align*}
x y^{\prime }+y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.796 |
|
| 23137 |
\begin{align*}
y^{\prime }&=1+\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.797 |
|
| 23138 |
\begin{align*}
x^{2}+y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.799 |
|
| 23139 |
\begin{align*}
\left (x^{2} y \sin \left (y x \right )-4 x \right ) y^{\prime }+x y^{2} \sin \left (y x \right )-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.800 |
|
| 23140 |
\begin{align*}
y^{\prime \prime }-\left (\frac {f^{\prime }\left (x \right )}{f \left (x \right )}+2 a \right ) y^{\prime }+\left (\frac {f^{\prime }\left (x \right ) a}{f \left (x \right )}+a^{2}-b^{2} f \left (x \right )^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.804 |
|
| 23141 |
\begin{align*}
2 y^{\prime \prime }&=a \,{\mathrm e}^{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.805 |
|
| 23142 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.809 |
|
| 23143 |
\begin{align*}
5 x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y&=\sqrt {x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.813 |
|
| 23144 |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.814 |
|
| 23145 |
\begin{align*}
y^{2} \left (x y^{\prime }+y\right ) \sqrt {x^{4}+1}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.826 |
|
| 23146 |
\begin{align*}
x -y-1+\left (y-x +2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.826 |
|
| 23147 |
\begin{align*}
\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=1+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.833 |
|
| 23148 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} x & 0\le x \le \pi \\ 0 & \pi <x \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.834 |
|
| 23149 |
\begin{align*}
y y^{\prime }-7 y&=6 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.835 |
|
| 23150 |
\begin{align*}
y^{\prime }&=3 x^{2} \left (y+2\right ) \\
y \left (2\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.835 |
|
| 23151 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+2 \left (1-x \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.841 |
|
| 23152 |
\begin{align*}
y-2 x y^{\prime }&={y^{\prime }}^{2} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.846 |
|
| 23153 |
\begin{align*}
{y^{\prime }}^{2} x^{2}+y^{2}-y^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.852 |
|
| 23154 |
\begin{align*}
-\csc \left (x \right )^{2} y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.854 |
|
| 23155 |
\begin{align*}
y^{\prime }+y \cot \left (x \right )&=y^{4} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.859 |
|
| 23156 |
\begin{align*}
y^{\prime }+t^{2}&=y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.862 |
|
| 23157 |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )-2 y \sin \left (x \right )+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.863 |
|
| 23158 |
\begin{align*}
y^{\prime }&=\frac {x^{3}+x^{2} y+3 y^{3}}{x^{3}+3 x y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.865 |
|
| 23159 |
\begin{align*}
r^{\prime }&=\frac {\sin \left (t \right )+{\mathrm e}^{r} \sin \left (t \right )}{3 \,{\mathrm e}^{r}+{\mathrm e}^{r} \cos \left (2 t \right )} \\
r \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.866 |
|
| 23160 |
\begin{align*}
y^{\prime } \sqrt {x^{4}+x^{2}+1}&=\sqrt {1+y^{2}+y^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.870 |
|
| 23161 |
\begin{align*}
2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.870 |
|
| 23162 |
\begin{align*}
y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.872 |
|
| 23163 |
\begin{align*}
x^{\prime }&=t -x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.874 |
|
| 23164 |
\begin{align*}
\frac {-x y^{\prime }+y}{\left (x +y\right )^{2}}+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.874 |
|
| 23165 |
\begin{align*}
y^{\prime }&=y^{2}+a \sinh \left (\beta x \right ) y+a b \sinh \left (\beta x \right )-b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.877 |
|
| 23166 |
\begin{align*}
\frac {x y^{\prime }+y}{1-x^{2} y^{2}}+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.882 |
|
| 23167 |
\begin{align*}
x^{\left (5\right )}+x&=0 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
8.886 |
|
| 23168 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a b \,x^{n +m}+b \left (m +1\right ) x^{m -1}-a \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
8.889 |
|
| 23169 |
\begin{align*}
2 x \left (1+\sqrt {x^{2}-y}\right )&=\sqrt {x^{2}-y}\, y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.892 |
|
| 23170 |
\begin{align*}
t^{2} y^{\prime }&=y^{2}+y t +t^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.897 |
|
| 23171 |
\begin{align*}
x +y+1+\left (2 x +2 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.900 |
|
| 23172 |
\begin{align*}
\left (y x +1\right ) y&=x y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.911 |
|
| 23173 |
\begin{align*}
x \left (1-2 x \right ) y^{\prime }&=4 x -\left (1+4 x \right ) y+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.914 |
|
| 23174 |
\begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.914 |
|
| 23175 |
\begin{align*}
x y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.917 |
|
| 23176 |
\begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (y\right )-1+\ln \left (x \right )+x^{3} \ln \left (x \right )^{2}+2 x^{3} \ln \left (y\right ) \ln \left (x \right )+x^{3} \ln \left (y\right )^{2}\right )}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.921 |
|
| 23177 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\delta \left (t -\pi \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. |
✓ |
✓ |
✓ |
✓ |
8.927 |
|
| 23178 |
\begin{align*}
x \sinh \left (y\right ) y^{\prime }&=\cosh \left (y\right ) \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.928 |
|
| 23179 |
\begin{align*}
b y+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.931 |
|
| 23180 |
\begin{align*}
x \cos \left (y\right ) y^{\prime }&=1+\sin \left (y\right ) \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.933 |
|
| 23181 |
\begin{align*}
\frac {2 y^{{3}/{2}}+1}{\sqrt {x}}+\left (3 \sqrt {x}\, \sqrt {y}-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.937 |
|
| 23182 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+y&=\frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.940 |
|
| 23183 |
\begin{align*}
y^{2} y^{\prime }&=x \\
y \left (-1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.951 |
|
| 23184 |
\begin{align*}
2 x^{2}-y \,{\mathrm e}^{x}-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.955 |
|
| 23185 |
\begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.957 |
|
| 23186 |
\begin{align*}
y y^{\prime }&=a x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.958 |
|
| 23187 |
\begin{align*}
\left (2 \sin \left (y\right )-x \right ) y^{\prime }&=\tan \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.968 |
|
| 23188 |
\begin{align*}
x y^{\prime }&=k y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.968 |
|
| 23189 |
\begin{align*}
y^{\prime }&=\frac {y^{2} f^{\prime }\left (x \right )}{g \left (x \right )}-\frac {g^{\prime }\left (x \right )}{f \left (x \right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.971 |
|
| 23190 |
\begin{align*}
x^{n} y^{\prime }-a y^{2}-b \,x^{2 n -2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.977 |
|
| 23191 |
\begin{align*}
y^{\prime }+\cos \left (\frac {x}{2}+\frac {y}{2}\right )&=\cos \left (\frac {x}{2}-\frac {y}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.983 |
|
| 23192 |
\begin{align*}
x y^{\prime }-2 y&=2 x^{4} \\
y \left (2\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.984 |
|
| 23193 |
\begin{align*}
y^{\prime }&=\frac {1}{y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.984 |
|
| 23194 |
\begin{align*}
y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x}+\frac {y}{x^{3}}&=\frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
8.987 |
|
| 23195 |
\begin{align*}
2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-4}} \\
y \left (3\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.989 |
|
| 23196 |
\begin{align*}
y+x \left (y^{2}+\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.990 |
|
| 23197 |
\begin{align*}
x y^{\prime }-y&=\sqrt {9 x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.997 |
|
| 23198 |
\begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.999 |
|
| 23199 |
\begin{align*}
2 x \sqrt {1-y^{2}}&=\left (x^{2}+1\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.001 |
|
| 23200 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }-4 x y^{\prime }+5 y&=\cos \left (x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.013 |
|