| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 22101 |
\begin{align*}
4 {y^{\prime }}^{2} x^{2}-y^{2}&=x y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.677 |
|
| 22102 |
\begin{align*}
y^{\prime }&=8 y x +3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.680 |
|
| 22103 |
\begin{align*}
y^{\prime }&=\frac {\left (-256 a \,x^{2} y-32 a^{2} x^{6}-256 a \,x^{2}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512 y+64 a \,x^{4}+512} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.681 |
|
| 22104 |
\begin{align*}
x^{\prime }&=\frac {\left (4+2 t \right ) x}{\ln \left (x\right )} \\
x \left (0\right ) &= {\mathrm e} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.681 |
|
| 22105 |
\begin{align*}
x y^{2} y^{\prime }&=x^{3}+y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.684 |
|
| 22106 |
\begin{align*}
2 x^{\prime }-\frac {x}{y}+x^{3} \cos \left (y \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.685 |
|
| 22107 |
\begin{align*}
\cos \left (x +y\right )-x \sin \left (x +y\right )&=x \sin \left (x +y\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.687 |
|
| 22108 |
\begin{align*}
y^{\prime \prime }&={\mathrm e}^{2 y} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.688 |
|
| 22109 |
\begin{align*}
\left (x \left (x +y\right )+a^{2}\right ) y^{\prime }&=y \left (x +y\right )+b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.691 |
|
| 22110 |
\begin{align*}
y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.691 |
|
| 22111 |
\begin{align*}
{y^{\prime }}^{2} x&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.691 |
|
| 22112 |
\begin{align*}
x y^{2} y^{\prime }&=x^{3}+y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.692 |
|
| 22113 |
\begin{align*}
x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (m +1\right )}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.694 |
|
| 22114 |
\begin{align*}
2 y t +y^{\prime }&=16 t \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.694 |
|
| 22115 |
\begin{align*}
2 x +3 y+2+\left (-x +y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.699 |
|
| 22116 |
\begin{align*}
y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.701 |
|
| 22117 |
\begin{align*}
y^{\prime }&=\left (x +y+1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.703 |
|
| 22118 |
\begin{align*}
\left (2 x +1\right ) y^{\prime }&=4 \,{\mathrm e}^{-y}-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.704 |
|
| 22119 |
\begin{align*}
5 x +3 \,{\mathrm e}^{y}+2 x \,{\mathrm e}^{y} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.704 |
|
| 22120 |
\begin{align*}
x^{2} y^{\prime }&=y \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.706 |
|
| 22121 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x +x^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.708 |
|
| 22122 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\sin \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.710 |
|
| 22123 |
\begin{align*}
y^{\prime }-x^{a -1} y^{1-b} f \left (\frac {x^{a}}{a}+\frac {y^{b}}{b}\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.713 |
|
| 22124 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+b \,x^{m} y+b c \,x^{m}-a \,c^{2} x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.713 |
|
| 22125 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.713 |
|
| 22126 |
\begin{align*}
2 x +\frac {x^{2}+y^{2}}{x^{2} y}&=\frac {\left (x^{2}+y^{2}\right ) y^{\prime }}{x y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.714 |
|
| 22127 |
\begin{align*}
1+y x -\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.717 |
|
| 22128 |
\begin{align*}
1+y^{2}&=x y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.719 |
|
| 22129 |
\begin{align*}
3 {y^{\prime }}^{2}+4 x y^{\prime }+x^{2}-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.720 |
|
| 22130 |
\begin{align*}
y&=a y^{\prime }+b {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.723 |
|
| 22131 |
\begin{align*}
\left (y x +1\right ) y-x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.723 |
|
| 22132 |
\begin{align*}
\left (t +1\right ) y+t y^{\prime }&=2 t \,{\mathrm e}^{-t} \\
y \left (1\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.724 |
|
| 22133 |
\begin{align*}
{\mathrm e}^{x}-\left (1+{\mathrm e}^{x}\right ) y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.725 |
|
| 22134 |
\begin{align*}
x y^{2} y^{\prime }-y^{3}&=\frac {x^{4}}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.727 |
|
| 22135 |
\begin{align*}
a^{2} {y^{\prime \prime }}^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.729 |
|
| 22136 |
\begin{align*}
y-\left (x +1\right ) y^{\prime }+2 \left (x +1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.731 |
|
| 22137 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.732 |
|
| 22138 |
\begin{align*}
\sin \left (x \right )^{2} y^{\prime }+\sin \left (x \right )^{2}+\left (x +y\right ) \sin \left (2 x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.733 |
|
| 22139 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+\lambda x y+a \,b^{2} x^{n} {\mathrm e}^{\lambda \,x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.736 |
|
| 22140 |
\begin{align*}
\sin \left (x \right )+\cos \left (y\right )+\cos \left (x \right )-y^{\prime } \sin \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.737 |
|
| 22141 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.737 |
|
| 22142 |
\begin{align*}
3 x y^{4} {y^{\prime }}^{2}-y^{5} y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.739 |
|
| 22143 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
y \left (0\right ) &= 10 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.740 |
|
| 22144 |
\begin{align*}
\ln \left (x \right ) y^{\prime \prime }-y \sin \left (x \right )&=0 \\
y \left ({\mathrm e}\right ) &= {\mathrm e}^{-1} \\
y^{\prime }\left ({\mathrm e}\right ) &= 0 \\
\end{align*}
Series expansion around \(x={\mathrm e}\). |
✓ |
✓ |
✓ |
✓ |
6.742 |
|
| 22145 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.743 |
|
| 22146 |
\begin{align*}
y^{\prime }+\sin \left (\frac {x}{2}+\frac {y}{2}\right )&=\sin \left (\frac {x}{2}-\frac {y}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.744 |
|
| 22147 |
\begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.744 |
|
| 22148 |
\begin{align*}
y^{\prime }&=\frac {y+x \,{\mathrm e}^{-\frac {y}{x}}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.746 |
|
| 22149 |
\begin{align*}
x \left (y+1\right ) y^{\prime }-\left (1-x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.747 |
|
| 22150 |
\begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.747 |
|
| 22151 |
\begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.748 |
|
| 22152 |
\begin{align*}
y^{2}+x y y^{\prime }&=\left (2 y^{2}+1\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.748 |
|
| 22153 |
\begin{align*}
{\mathrm e}^{y x} \left (x^{4} y+4 x^{3}\right )+3 y+\left (x^{5} {\mathrm e}^{y x}+3 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.749 |
|
| 22154 |
\begin{align*}
y^{\prime }&=3 y-3 x +3+\left (x -y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.749 |
|
| 22155 |
\begin{align*}
y^{\prime }&=-\frac {t}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.750 |
|
| 22156 |
\begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.751 |
|
| 22157 |
\begin{align*}
x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.752 |
|
| 22158 |
\begin{align*}
2 \left (1-y\right ) y y^{\prime \prime }&=\left (1-3 y\right ) {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.753 |
|
| 22159 |
\begin{align*}
x^{\prime }+2 x y&={\mathrm e}^{-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.754 |
|
| 22160 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y+g \left (x \right ) y^{k} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.759 |
|
| 22161 |
\begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+y^{2}&=x^{2} y^{2}+x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.759 |
|
| 22162 |
\begin{align*}
-y+x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=x \left (-x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.760 |
|
| 22163 |
\begin{align*}
x y^{\prime }+\tan \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.762 |
|
| 22164 |
\begin{align*}
x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+8 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.762 |
|
| 22165 |
\begin{align*}
y^{\prime \prime }+a x y^{\prime }+b x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.762 |
|
| 22166 |
\begin{align*}
y^{\prime }&=\sqrt {-x +y}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.764 |
|
| 22167 |
\begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.766 |
|
| 22168 |
\begin{align*}
y^{\prime }&=\frac {\textit {\_F1} \left (y^{2}-2 \ln \left (x \right )\right )}{\sqrt {y^{2}}\, x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.769 |
|
| 22169 |
\begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.769 |
|
| 22170 |
\begin{align*}
y y^{\prime }+x y^{2}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.770 |
|
| 22171 |
\begin{align*}
y^{\prime }&=-x -\sqrt {x^{2}+2 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.770 |
|
| 22172 |
\begin{align*}
\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.771 |
|
| 22173 |
\begin{align*}
y^{\prime }+x^{2} \left (y+1\right ) \left (-2+y\right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.773 |
|
| 22174 |
\begin{align*}
y^{\prime }&=\frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \\
y \left (0\right ) &= 100 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.773 |
|
| 22175 |
\begin{align*}
\cos \left (x \right )^{2} y^{\prime }+y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.773 |
|
| 22176 |
\begin{align*}
y^{\prime }&=a +b \sin \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.777 |
|
| 22177 |
\begin{align*}
3 x^{2} y^{\prime }+2 x^{2}-3 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.783 |
|
| 22178 |
\begin{align*}
y^{\prime }&=\frac {x^{4}+2 y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.783 |
|
| 22179 |
\begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }-x +y \left (y+1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.784 |
|
| 22180 |
\begin{align*}
x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.785 |
|
| 22181 |
\begin{align*}
y^{\prime }&=\frac {2 t^{5}}{5 y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.786 |
|
| 22182 |
\begin{align*}
8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.787 |
|
| 22183 |
\begin{align*}
x \left (1-y^{3}\right )-3 y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.789 |
|
| 22184 |
\begin{align*}
x^{\prime }&=\sqrt {1-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.789 |
|
| 22185 |
\begin{align*}
y^{\prime }-a \left (\tan \left (y\right )^{2}+1\right )+\tan \left (y\right ) \tan \left (x \right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
6.791 |
|
| 22186 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (-a^{2} \cos \left (x \right )^{2}-\left (3-2 a \right ) \cos \left (x \right )-3+3 a \right ) y}{\sin \left (x \right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.793 |
|
| 22187 |
\begin{align*}
y x^{\prime }&=2 y \,{\mathrm e}^{3 y}+x \left (3 y +2\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.794 |
|
| 22188 |
\begin{align*}
y y^{\prime }+x&=\frac {\left (x^{2}+y^{2}\right )^{2}}{2 x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.794 |
|
| 22189 |
\begin{align*}
y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.795 |
|
| 22190 |
\begin{align*}
a y^{\prime \prime } y^{\prime \prime \prime }&=\sqrt {1+{y^{\prime \prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.796 |
|
| 22191 |
\begin{align*}
y^{\prime }&=\left (a +b x +c y\right )^{6} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.796 |
|
| 22192 |
\begin{align*}
y^{\prime }&=\frac {y \left (1-x +y \ln \left (x \right ) x^{2}+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (x -1\right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.798 |
|
| 22193 |
\begin{align*}
3 \left (x^{2}-1\right ) y+\left (x^{3}+8 y-3 x \right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.798 |
|
| 22194 |
\begin{align*}
x y^{\prime }+2 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.799 |
|
| 22195 |
\begin{align*}
y^{\prime }-x y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.801 |
|
| 22196 |
\begin{align*}
{y^{\prime }}^{2}&=4 y^{3} \left (1-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.802 |
|
| 22197 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=\frac {4 x^{2} \cos \left (x \right )}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.803 |
|
| 22198 |
\begin{align*}
y^{\prime }&=\frac {\left (-y^{2}+4 a x \right )^{2}}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.803 |
|
| 22199 |
\begin{align*}
c v^{\prime \prime }+\frac {v^{\prime }}{r}+\frac {v}{L}&=\delta \left (t -1\right )-\delta \left (t \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.803 |
|
| 22200 |
\begin{align*}
x y y^{\prime }-y^{2}&=1 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.803 |
|