| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 22101 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (-2\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.337 |
|
| 22102 |
\begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.339 |
|
| 22103 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \left ({\mathrm e}^{x}-{\mathrm e}^{y}\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
9.343 |
|
| 22104 |
\begin{align*}
x -y+3+\left (3 x +y+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.344 |
|
| 22105 |
\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*} |
✓ |
✓ |
✓ |
✓ |
9.351 |
|
| 22106 |
\begin{align*}
\left (2 x -2 y+5\right ) y^{\prime }-x +y-3&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.358 |
|
| 22107 |
\begin{align*}
y^{\prime }&=\frac {x}{y}-\frac {x}{1+y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.362 |
|
| 22108 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.364 |
|
| 22109 |
\begin{align*}
8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.370 |
|
| 22110 |
\begin{align*}
y+\left (y^{n} a \,x^{2}-2 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.373 |
|
| 22111 |
\begin{align*}
y^{\prime }&=4 t^{2}-t y^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.380 |
|
| 22112 |
\begin{align*}
x -y+\left (y-x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.381 |
|
| 22113 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+3 y&=\delta \left (t -1\right )-3 \delta \left (t -4\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
9.382 |
|
| 22114 |
\begin{align*}
y^{\prime }&=\frac {x +y+1}{2 x +2 y-1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.389 |
|
| 22115 |
\begin{align*}
y^{\prime \prime }+\left (x^{n} a b +b \,x^{n -1}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{n}+1\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
9.394 |
|
| 22116 |
\begin{align*}
x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.395 |
|
| 22117 |
\begin{align*}
y^{\prime }&=\frac {2}{x +2 y-3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.396 |
|
| 22118 |
\begin{align*}
2 y^{\prime } x -y+\frac {x^{2}}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.398 |
|
| 22119 |
\begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.401 |
|
| 22120 |
\begin{align*}
x +\sin \left (x \right )+\sin \left (y\right )+y^{\prime } \cos \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.402 |
|
| 22121 |
\begin{align*}
y+6 x y^{3}-4 y^{4}-\left (2 x +4 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.402 |
|
| 22122 |
\begin{align*}
y^{\prime }&=\frac {2 y x -y^{4}}{3 x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.405 |
|
| 22123 |
\begin{align*}
y^{\prime }&=-\frac {a x}{2}-\frac {b}{2}+x \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.406 |
|
| 22124 |
\begin{align*}
{\mathrm e}^{x} y^{\prime }&=2 x y^{2}+{\mathrm e}^{x} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.407 |
|
| 22125 |
\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*} |
✓ |
✓ |
✓ |
✗ |
9.408 |
|
| 22126 |
\begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.413 |
|
| 22127 |
\begin{align*}
\frac {1}{2 \sqrt {t}}+y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.414 |
|
| 22128 |
\begin{align*}
y^{\prime }&=\sqrt {1+6 x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.421 |
|
| 22129 |
\begin{align*}
\left (1+{y^{\prime }}^{2}\right ) \sin \left (-y+y^{\prime } x \right )^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.422 |
|
| 22130 |
\begin{align*}
x^{n} y^{\prime \prime }+\left (a \,x^{n +m}+1\right ) y^{\prime }+a \,x^{m} \left (1+m \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
9.422 |
|
| 22131 |
\begin{align*}
y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right )&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.427 |
|
| 22132 |
\begin{align*}
y^{\prime }&=z \\
z^{\prime }&=w \\
w^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.432 |
|
| 22133 |
\begin{align*}
y^{\prime }&=\frac {x +3 y}{-3 x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.435 |
|
| 22134 |
\begin{align*}
y^{\prime }-f_{3} \left (x \right ) y^{3}-f_{2} \left (x \right ) y^{2}-f_{1} \left (x \right ) y-f_{0} \left (x \right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
9.438 |
|
| 22135 |
\begin{align*}
y^{\prime }+y x&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.443 |
|
| 22136 |
\begin{align*}
{y^{\prime \prime }}^{2}&=a +b {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.447 |
|
| 22137 |
\begin{align*}
y^{\prime }&=\frac {-3+x +y}{y-x +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.449 |
|
| 22138 |
\begin{align*}
\left (x +y^{2}\right ) y^{\prime \prime }-2 \left (x -y^{2}\right ) {y^{\prime }}^{3}+y^{\prime } \left (1+4 y y^{\prime }\right )&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
9.456 |
|
| 22139 |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.461 |
|
| 22140 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-x^{2} y&=\left (x +1\right ) \sqrt {-x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.464 |
|
| 22141 |
\begin{align*}
y^{\prime }-y^{3}-a \,{\mathrm e}^{x} y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.464 |
|
| 22142 |
\begin{align*}
\left (x -a \right ) \left (-b +x \right ) y^{\prime }&=c y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.467 |
|
| 22143 |
\begin{align*}
\frac {y^{5} x^{2}+y^{2}+y}{1+x^{2} y^{4}}+\frac {\left (x^{3} y^{4}+2 y x +x \right ) y^{\prime }}{1+x^{2} y^{4}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.471 |
|
| 22144 |
\begin{align*}
\left (c \,x^{2}+b \right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.474 |
|
| 22145 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.475 |
|
| 22146 |
\begin{align*}
x +y-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.475 |
|
| 22147 |
\begin{align*}
y y^{\prime }&=b \cos \left (x +c \right )+a y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.479 |
|
| 22148 |
\begin{align*}
x {y^{\prime }}^{2}+\left (-3 x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.483 |
|
| 22149 |
\begin{align*}
y^{\prime } x +y \ln \left (x \right )&=y \ln \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.490 |
|
| 22150 |
\begin{align*}
y^{\prime } x +y&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.490 |
|
| 22151 |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )-2 \sin \left (x \right ) y+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.496 |
|
| 22152 |
\begin{align*}
y^{\prime } x +y&=x^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.497 |
|
| 22153 |
\begin{align*}
y^{\prime \prime } \cos \left (y\right )+\left (\cos \left (y\right )-y^{\prime } \sin \left (y\right )\right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
9.501 |
|
| 22154 |
\begin{align*}
y^{\prime }&=\frac {x^{2}-3 y^{2}}{2 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.507 |
|
| 22155 |
\begin{align*}
y^{\prime }&=y^{2} {\mathrm e}^{-t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.510 |
|
| 22156 |
\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 (2+x \right ) y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.511 |
|
| 22157 |
\begin{align*}
\left (a -x \right ) y^{\prime }&=y+\left (c x +b \right ) y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.512 |
|
| 22158 |
\begin{align*}
x^{\prime }&=t^{2} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.519 |
|
| 22159 |
\begin{align*}
y^{2}+\left (x^{2}+3 y x +4 y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.527 |
|
| 22160 |
\begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.541 |
|
| 22161 |
\begin{align*}
y^{\prime } x -2 y&=x^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.542 |
|
| 22162 |
\begin{align*}
y^{\prime }&=\left (1+y^{2}\right ) \tan \left (x \right ) \\
y \left (0\right ) &= \sqrt {3} \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
9.556 |
|
| 22163 |
\begin{align*}
\left (u^{2}+1\right ) v^{\prime }+4 u v&=3 u \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.557 |
|
| 22164 |
\begin{align*}
{y^{\prime }}^{2}&=\left (4 y+1\right ) \left (y^{\prime }-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.559 |
|
| 22165 |
\begin{align*}
y^{\prime }&=\frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x^{2}}{\left (x -1\right ) \left (x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.563 |
|
| 22166 |
\begin{align*}
\left (x +1\right ) y^{\prime }-1-y&=\left (x +1\right ) \sqrt {1+y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.567 |
|
| 22167 |
\begin{align*}
y^{\prime }&=\sqrt {2 x +3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.570 |
|
| 22168 |
\begin{align*}
\left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.576 |
|
| 22169 |
\begin{align*}
1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.576 |
|
| 22170 |
\begin{align*}
y^{\prime \prime }&=c \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.578 |
|
| 22171 |
\begin{align*}
f \left (x \right ) y^{m} y^{\prime }+g \left (x \right ) y^{m +1}+h \left (x \right ) y^{n}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.582 |
|
| 22172 |
\begin{align*}
y^{\prime }&=a y-b y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.584 |
|
| 22173 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda \arccos \left (x \right )^{n} y-a^{2}+a \lambda \arccos \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.590 |
|
| 22174 |
\begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.598 |
|
| 22175 |
\begin{align*}
y^{\prime }&=\left (a \,{\mathrm e}^{x}+y\right ) y^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.601 |
|
| 22176 |
\begin{align*}
\left (x -y\right )^{2} y^{\prime }&=\left (-x -y+1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.603 |
|
| 22177 |
\begin{align*}
x^{5} y^{\prime }+y^{5}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.604 |
|
| 22178 |
\begin{align*}
y^{\prime }&=\frac {x^{3} y+x^{3}+x y^{2}+y^{3}}{\left (x -1\right ) x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.607 |
|
| 22179 |
\begin{align*}
y^{\prime }&=\frac {y x +x +y^{2}}{\left (x -1\right ) \left (x +y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.611 |
|
| 22180 |
\begin{align*}
y^{\prime }-\frac {3 y}{x -1}&=\left (x -1\right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.611 |
|
| 22181 |
\begin{align*}
y^{\prime }&=\frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.612 |
|
| 22182 |
\begin{align*}
x^{3} y^{\prime }-\cos \left (y\right )&=1 \\
y \left (\infty \right ) &= 5 \pi \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
9.613 |
|
| 22183 |
\begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.631 |
|
| 22184 |
\begin{align*}
y^{4}-2 y x +3 x^{2} y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.631 |
|
| 22185 |
\begin{align*}
y^{\prime } \sqrt {b^{2}+y^{2}}&=\sqrt {a^{2}+x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.633 |
|
| 22186 |
\begin{align*}
x^{4} y^{\prime }+a^{2}+y^{2} x^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.638 |
|
| 22187 |
\begin{align*}
y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.638 |
|
| 22188 |
\begin{align*}
y^{\prime } t +y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.640 |
|
| 22189 |
\begin{align*}
\left (2 a y^{3}+3 a x y^{2}-b \,x^{3}+c \,x^{2}\right ) y^{\prime }-a y^{3}+c y^{2}+3 b \,x^{2} y+2 b \,x^{3}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.641 |
|
| 22190 |
\begin{align*}
y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.642 |
|
| 22191 |
\begin{align*}
y^{\prime }&=x \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.644 |
|
| 22192 |
\begin{align*}
x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.649 |
|
| 22193 |
\begin{align*}
\left (x^{2}-1\right ) y+\left (1+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.649 |
|
| 22194 |
\begin{align*}
\sin \left (y\right )+\sin \left (x \right ) y+\frac {1}{x}+\left (x \cos \left (y\right )-\cos \left (x \right )+\frac {1}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.659 |
|
| 22195 |
\begin{align*}
y^{\prime }&=\frac {y \left (-1-x \,{\mathrm e}^{\frac {x +1}{x -1}}+x^{2} {\mathrm e}^{\frac {x +1}{x -1}} y-x^{2} {\mathrm e}^{\frac {x +1}{x -1}}+x^{3} {\mathrm e}^{\frac {x +1}{x -1}} y\right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.661 |
|
| 22196 |
\begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.664 |
|
| 22197 |
\begin{align*}
x \left (1-2 x \right ) y^{\prime }&=4 x -\left (4 x +1\right ) y+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.668 |
|
| 22198 |
\begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.674 |
|
| 22199 |
\begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.679 |
|
| 22200 |
\begin{align*}
x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+a^{2} x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.685 |
|