| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 24201 |
\begin{align*}
y^{\prime }&=\frac {y x +y+x^{4} \sqrt {x^{2}+y^{2}}}{x \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
12.446 |
|
| 24202 |
\begin{align*}
\left (2+3 x -y x \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.446 |
|
| 24203 |
\begin{align*}
\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=r y^{\prime \prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.451 |
|
| 24204 |
\begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.452 |
|
| 24205 |
\begin{align*}
y^{\prime }&=-8 x y^{2}+4 x \left (1+4 x \right ) y-8 x^{3}-4 x^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.453 |
|
| 24206 |
\begin{align*}
x^{2}+y^{2}+3 x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.454 |
|
| 24207 |
\begin{align*}
x y^{\prime }+3 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.454 |
|
| 24208 |
\begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.455 |
|
| 24209 |
\begin{align*}
x -y-2-\left (2 x -2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.457 |
|
| 24210 |
\begin{align*}
1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.459 |
|
| 24211 |
\begin{align*}
y y^{\prime }+1&=\left (x -1\right ) {\mathrm e}^{-\frac {y^{2}}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.467 |
|
| 24212 |
\begin{align*}
{y^{\prime }}^{3}+{\mathrm e}^{3 x -2 y} \left (y^{\prime }-1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
12.476 |
|
| 24213 |
\begin{align*}
x y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
12.479 |
|
| 24214 |
\begin{align*}
\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right )&=\left (\cos \left (x \right )-\sin \left (x \right )\right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
12.487 |
|
| 24215 |
\begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.487 |
|
| 24216 |
\begin{align*}
x y^{\prime }&=y+2 x \,{\mathrm e}^{-\frac {y}{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.493 |
|
| 24217 |
\begin{align*}
y^{\prime }+\sqrt {\frac {1-y^{2}}{-x^{2}+1}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.499 |
|
| 24218 |
\begin{align*}
y+\left (2 x +y x -3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.502 |
|
| 24219 |
\begin{align*}
-x y^{\prime }+y&=y y^{\prime }+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.508 |
|
| 24220 |
\begin{align*}
2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.522 |
|
| 24221 |
\begin{align*}
y^{\prime }&=\frac {y^{3}-2 x^{3}}{x y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.529 |
|
| 24222 |
\begin{align*}
y x +y^{2}+x^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.531 |
|
| 24223 |
\begin{align*}
y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
12.534 |
|
| 24224 |
\begin{align*}
y^{\prime }&=\frac {y \left (x \ln \left (x \right )+\ln \left (x \right )+x \ln \left (y\right )+\ln \left (y\right )-x -1+x \ln \left (x \right )^{2}+2 x \ln \left (y\right ) \ln \left (x \right )+x \ln \left (y\right )^{2}\right )}{x \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
12.539 |
|
| 24225 |
\begin{align*}
y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.540 |
|
| 24226 |
\begin{align*}
y y^{\prime }+x&=m \left (x y^{\prime }-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.541 |
|
| 24227 |
\begin{align*}
y^{\prime }&=\left (-1+y\right ) \left (-2+y\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
12.544 |
|
| 24228 |
\begin{align*}
y^{\prime }&=\sqrt {y^{2}-9} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.550 |
|
| 24229 |
\begin{align*}
y^{\prime }&=\frac {F \left (\frac {a y^{2}+b \,x^{2}}{a}\right ) x}{\sqrt {a}\, y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.555 |
|
| 24230 |
\begin{align*}
\sec \left (x \right ) \cos \left (y\right )^{2}-\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.557 |
|
| 24231 |
\begin{align*}
x y^{\prime }+\cos \left (x^{2}\right )&=827 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.557 |
|
| 24232 |
\begin{align*}
x y^{\prime }&=y+x \sec \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.571 |
|
| 24233 |
\begin{align*}
y y^{\prime }+\tan \left (x \right ) y^{2}&=\cos \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.576 |
|
| 24234 |
\begin{align*}
y \left (1-y^{2} x^{4}\right )+x y^{\prime }&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.577 |
|
| 24235 |
\begin{align*}
x y^{\prime }+2&=x^{3} \left (-1+y\right ) y^{\prime } \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.579 |
|
| 24236 |
\begin{align*}
x y^{\prime }&=a y^{3}+3 a b \,x^{n} y^{2}-b n \,x^{n}-2 a \,b^{3} x^{3 n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.580 |
|
| 24237 |
\begin{align*}
\left (x^{2}-y\right ) y^{\prime }-4 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.586 |
|
| 24238 |
\begin{align*}
y^{\prime } \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}&=\sqrt {b_{0} +b_{1} y+b_{2} y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.587 |
|
| 24239 |
\begin{align*}
x^{2} \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.588 |
|
| 24240 |
\begin{align*}
x y^{\prime }+y&=x^{4} y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.591 |
|
| 24241 |
\begin{align*}
z^{\prime \prime }+z^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.592 |
|
| 24242 |
\begin{align*}
\left (a^{2} x^{2}+\left (x^{2}+y^{2}\right )^{2}\right ) y^{\prime }&=a^{2} x y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.599 |
|
| 24243 |
\begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
12.605 |
|
| 24244 |
\begin{align*}
x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n +2 m}-b^{2} x^{4 m +2}+a m \,x^{n -1}-m^{2}-m \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
12.613 |
|
| 24245 |
\begin{align*}
y^{\prime }&=\sqrt {2 x +3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.613 |
|
| 24246 |
\begin{align*}
x y^{\prime }-2 y&=\frac {x^{6}}{x^{2}+y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.619 |
|
| 24247 |
\begin{align*}
y^{\prime }&=\frac {y+x^{2} \ln \left (x \right )^{3}+2 x^{2} \ln \left (x \right )^{2} y+x^{2} \ln \left (x \right ) y^{2}}{x \ln \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.619 |
|
| 24248 |
\begin{align*}
\left (x -y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.620 |
|
| 24249 |
\begin{align*}
2 y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.621 |
|
| 24250 |
\begin{align*}
\left (x +2 y^{3}\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.625 |
|
| 24251 |
\begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=t^{7} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.627 |
|
| 24252 |
\begin{align*}
y^{\prime }&=x^{3}+y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
12.630 |
|
| 24253 |
\begin{align*}
\left (2 y^{2}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.638 |
|
| 24254 |
\begin{align*}
\left (1-3 y^{2}\right ) {y^{\prime }}^{2}+y \left (1+y^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.642 |
|
| 24255 |
\begin{align*}
\left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (a_{1} x +b_{1} \right ) y+a_{0} x +b_{0}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.653 |
|
| 24256 |
\begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.655 |
|
| 24257 |
\begin{align*}
y-\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.655 |
|
| 24258 |
\begin{align*}
x^{2} y^{\prime }&=y^{2}+y x -4 x^{2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.665 |
|
| 24259 |
\begin{align*}
t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y&=\ln \left (t \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
12.681 |
|
| 24260 |
\begin{align*}
y^{\prime }&=\frac {\left (x -y\right )^{3} \left (x +y\right )^{3} x}{\left (x^{2}-y^{2}-1\right ) y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.682 |
|
| 24261 |
\begin{align*}
y^{\prime }&=\frac {x -y+2}{x +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.687 |
|
| 24262 |
\begin{align*}
y^{\prime }&=y^{2}-x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.688 |
|
| 24263 |
\begin{align*}
x y y^{\prime }&=a +b y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.694 |
|
| 24264 |
\begin{align*}
2+y^{2}-\left (y x +2 y+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.694 |
|
| 24265 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= {\frac {1}{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.695 |
|
| 24266 |
\begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.697 |
|
| 24267 |
\begin{align*}
y^{\prime }&=-\frac {x}{2}+1+\sqrt {x^{2}-4 x +4 y}+x^{2} \sqrt {x^{2}-4 x +4 y}+x^{3} \sqrt {x^{2}-4 x +4 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
12.706 |
|
| 24268 |
\begin{align*}
y^{\prime }&=\frac {\left (y-\operatorname {Si}\left (x \right )\right )^{2}+\sin \left (x \right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.708 |
|
| 24269 |
\begin{align*}
x y^{\prime }-y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.714 |
|
| 24270 |
\begin{align*}
{y^{\prime }}^{2} x +y y^{\prime }-x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.714 |
|
| 24271 |
\begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.717 |
|
| 24272 |
\begin{align*}
x +2 y-1+3 \left (x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.718 |
|
| 24273 |
\begin{align*}
y^{\prime }&=\left (1+y^{2}\right ) \tan \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.720 |
|
| 24274 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.721 |
|
| 24275 |
\begin{align*}
x +y+\left (x +2 y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.725 |
|
| 24276 |
\begin{align*}
y^{3}+\left (3 x^{2}-2 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.731 |
|
| 24277 |
\begin{align*}
3 t -y+1-\left (6 t -2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.731 |
|
| 24278 |
\begin{align*}
y^{4}+y x +\left (x y^{3}-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.735 |
|
| 24279 |
\begin{align*}
y y^{\prime }+x&=m \left (x y^{\prime }-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.747 |
|
| 24280 |
\begin{align*}
y^{\prime }&=\frac {-4 y x -x^{3}-2 a \,x^{2}-4 x +8}{8 y+2 x^{2}+4 a x +8} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.749 |
|
| 24281 |
\begin{align*}
y^{\prime }+\frac {y}{2 x}&=\frac {x}{y^{3}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.752 |
|
| 24282 |
\begin{align*}
y^{\prime }&=\frac {x -\cos \left (x \right ) y}{\sin \left (x \right )+y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.754 |
|
| 24283 |
\begin{align*}
y^{\prime }&=\frac {x^{2} y^{2}+2 y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.755 |
|
| 24284 |
\begin{align*}
4 x^{2}-y x +y^{2}+y^{\prime } \left (x^{2}-y x +4 y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.755 |
|
| 24285 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.765 |
|
| 24286 |
\begin{align*}
y^{\prime }&=\sqrt {y^{2}-9} \\
y \left (5\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.765 |
|
| 24287 |
\begin{align*}
y^{\prime }&=\frac {2 x}{x -y+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.766 |
|
| 24288 |
\begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.769 |
|
| 24289 |
\begin{align*}
b y+\left (x +a \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
12.780 |
|
| 24290 |
\begin{align*}
-a y+\left (c -x \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
12.783 |
|
| 24291 |
\begin{align*}
y^{\prime \prime }&=a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.789 |
|
| 24292 |
\begin{align*}
y \left (y^{2}+2 x \right )+x \left (y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.813 |
|
| 24293 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.817 |
|
| 24294 |
\begin{align*}
x y y^{\prime }&=3 x^{2}+4 y^{2} \\
y \left (1\right ) &= \sqrt {3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.819 |
|
| 24295 |
\begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.821 |
|
| 24296 |
\begin{align*}
\left (y+1\right ) y^{\prime }+x \left (y^{2}+2 y\right )&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.825 |
|
| 24297 |
\begin{align*}
y y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.827 |
|
| 24298 |
\begin{align*}
y^{\prime }&=k y-c y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.830 |
|
| 24299 |
\begin{align*}
x^{2} y^{\prime \prime }-2 n x \left (x +1\right ) y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
12.832 |
|
| 24300 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (-4+t \right )+\operatorname {Heaviside}\left (t -6\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
12.833 |
|