| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 20301 |
\begin{align*}
2 t y^{3}+\left (1+3 y^{2} t^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.584 |
|
| 20302 |
\begin{align*}
y^{\prime }&=-F \left (x \right ) \left (-7 x y^{2}-x^{3}\right )+\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.585 |
|
| 20303 |
\begin{align*}
y^{\prime }&=2 x \left (\pi +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.585 |
|
| 20304 |
\begin{align*}
u \left (1-v \right )+v^{2} \left (1-u\right ) u^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.586 |
|
| 20305 |
\begin{align*}
y^{\prime }&=\frac {4 x \left (a -1\right ) \left (a +1\right )}{4 y+y^{4} a^{2}-2 a^{4} y^{2} x^{2}+4 y^{2} a^{2} x^{2}+a^{6} x^{4}-3 a^{4} x^{4}+3 a^{2} x^{4}-y^{4}-2 x^{2} y^{2}-x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.586 |
|
| 20306 |
\begin{align*}
y^{\prime }&=x \left (a y^{2}+b \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.588 |
|
| 20307 |
\begin{align*}
y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.588 |
|
| 20308 |
\begin{align*}
\operatorname {f3} \left (x \right ) y^{2}+\operatorname {f2} \left (x \right ) y y^{\prime }+\operatorname {f1} \left (x \right ) {y^{\prime }}^{2}+\operatorname {f0} \left (x \right ) y y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
4.589 |
|
| 20309 |
\begin{align*}
\left (-x^{2}+1\right ) y y^{\prime }+2 x^{2}+x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.590 |
|
| 20310 |
\begin{align*}
\left (x^{2}-y\right ) y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.591 |
|
| 20311 |
\begin{align*}
x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.593 |
|
| 20312 |
\begin{align*}
x^{2}+1+\left (y^{2}+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.593 |
|
| 20313 |
\begin{align*}
y^{\prime }&=\frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.594 |
|
| 20314 |
\begin{align*}
x y^{\prime }+x y^{2}-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.595 |
|
| 20315 |
\begin{align*}
y^{\prime }-y \sin \left (x \right )&=2 \sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.596 |
|
| 20316 |
\begin{align*}
y^{\prime }-6 y&={\mathrm e}^{6 t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.596 |
|
| 20317 |
\begin{align*}
x y^{\prime }+x^{2}-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.597 |
|
| 20318 |
\begin{align*}
y^{\prime }&=\sec \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.597 |
|
| 20319 |
\begin{align*}
y^{\prime \prime }+\omega ^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.598 |
|
| 20320 |
\begin{align*}
x^{\prime }&=x^{2}-3 x+2 \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.599 |
|
| 20321 |
\begin{align*}
\left (t^{2}+1\right ) s^{\prime }+2 t \left (s t^{2}-3 \left (t^{2}+1\right )^{2}\right )&=0 \\
s \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.599 |
|
| 20322 |
\begin{align*}
y^{\prime }-\frac {\sqrt {x^{2}-1}}{\sqrt {y^{2}-1}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.601 |
|
| 20323 |
\begin{align*}
y^{\prime }&=y f \left (t \right ) \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.602 |
|
| 20324 |
\begin{align*}
y^{\prime }&=-\frac {-x^{2}-y x -x^{3}-x y^{2}+2 y \ln \left (x \right ) x^{2}-x^{3} \ln \left (x \right )^{2}-y^{3}+3 x y^{2} \ln \left (x \right )-3 x^{2} \ln \left (x \right )^{2} y+x^{3} \ln \left (x \right )^{3}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.604 |
|
| 20325 |
\begin{align*}
a^{2} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.605 |
|
| 20326 |
\begin{align*}
y^{\prime }&=1-y+y^{2} {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.605 |
|
| 20327 |
\begin{align*}
\left (4 x^{2}-1\right ) y^{\prime \prime }+\left (4-\frac {2}{x}\right ) y^{\prime }+\frac {\left (-x^{2}+1\right ) y}{x^{2}+1}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.606 |
|
| 20328 |
\begin{align*}
-2+2 y+x^{2} \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.606 |
|
| 20329 |
\begin{align*}
y^{\prime }&=\frac {1+F \left (\frac {a x y+1}{a x}\right ) a \,x^{2}}{a \,x^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.607 |
|
| 20330 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.608 |
|
| 20331 |
\begin{align*}
\left (2 \,{\mathrm e}^{y}-x \right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.608 |
|
| 20332 |
\begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (x_{0} \right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.609 |
|
| 20333 |
\begin{align*}
i^{\prime }+3 i&=10 \sin \left (t \right ) \\
i \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.609 |
|
| 20334 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\left \{\begin {array}{cc} \sin \left (2 t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.611 |
|
| 20335 |
\begin{align*}
x \cos \left (x \right )+\left (1-6 y^{5}\right ) y^{\prime }&=0 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.611 |
|
| 20336 |
\begin{align*}
y^{\prime }&=\frac {y}{x -1}+x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.614 |
|
| 20337 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+3 x +2}{-2+y} \\
y \left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.615 |
|
| 20338 |
\begin{align*}
\sin \left (x \right ) y^{\prime }+y&=\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.615 |
|
| 20339 |
\begin{align*}
y x +2 x^{3} y+x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.615 |
|
| 20340 |
\begin{align*}
x y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.616 |
|
| 20341 |
\begin{align*}
2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.618 |
|
| 20342 |
\begin{align*}
x +\sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= \pi \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
4.620 |
|
| 20343 |
\begin{align*}
x^{2}+y \sin \left (y x \right )+x \sin \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.621 |
|
| 20344 |
\begin{align*}
y^{\prime }&=1-t +y^{2}-t y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.622 |
|
| 20345 |
\begin{align*}
x y^{\prime }+n y&=x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.622 |
|
| 20346 |
\begin{align*}
y^{\prime }&=\frac {\left (\ln \left (y\right )+x +x^{3}+x^{4}\right ) y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.622 |
|
| 20347 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.624 |
|
| 20348 |
\begin{align*}
y^{\prime }+\sin \left (y\right )+x \cos \left (y\right )+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.624 |
|
| 20349 |
\begin{align*}
\left (2 a^{2}-r^{2}\right ) r^{\prime }&=r^{3} \sin \left (\theta \right ) \\
r \left (0\right ) &= a \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
4.625 |
|
| 20350 |
\begin{align*}
1+y \tan \left (y x \right )+x \tan \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.625 |
|
| 20351 |
\begin{align*}
\tan \left (t \right ) y+y^{\prime }&=\tan \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.625 |
|
| 20352 |
\begin{align*}
s^{\prime \prime }&=-9 s \\
s \left (0\right ) &= 9 \\
s^{\prime }\left (0\right ) &= 18 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.626 |
|
| 20353 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ t & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.628 |
|
| 20354 |
\begin{align*}
x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.630 |
|
| 20355 |
\begin{align*}
x y^{\prime }+\left (\sin \left (y\right )-3 \cos \left (y\right ) x^{2}\right ) \cos \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.631 |
|
| 20356 |
\begin{align*}
x \left (1-x \right ) y^{\prime }&=a +2 \left (2-x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.631 |
|
| 20357 |
\begin{align*}
x^{n} y^{\prime \prime }+c \left (a x +b \right )^{n -4} y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
4.633 |
|
| 20358 |
\begin{align*}
x y^{\prime }+y&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.635 |
|
| 20359 |
\begin{align*}
\left (a \,x^{n}+b x +c \right ) y^{\prime \prime }&=a n \left (n -1\right ) x^{-2+n} y \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
4.635 |
|
| 20360 |
\begin{align*}
y^{\prime }+4 y&=t \,{\mathrm e}^{-4 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.636 |
|
| 20361 |
\begin{align*}
x \ln \left (x \right )^{2} y^{\prime }&=-4 \ln \left (x \right )^{2}+y \ln \left (x \right )+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.638 |
|
| 20362 |
\begin{align*}
y^{\prime }+y&=2 \sin \left (x \right )+5 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.639 |
|
| 20363 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=-1+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.640 |
|
| 20364 |
\begin{align*}
x^{3} \left (1+5 x^{3} y^{7}\right ) y^{\prime }+\left (3 x^{5} y^{5}-1\right ) y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.641 |
|
| 20365 |
\begin{align*}
3 x \left (x +y^{2}\right ) y^{\prime }+x^{3}-3 y x -2 y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.642 |
|
| 20366 |
\begin{align*}
r y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.644 |
|
| 20367 |
\begin{align*}
y^{\prime }&=\frac {3 t^{2}+4 t +2}{-2+2 y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.644 |
|
| 20368 |
\begin{align*}
y^{\prime }+y \,{\mathrm e}^{x}&=3 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.644 |
|
| 20369 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y \ln \left (\frac {1}{y}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.644 |
|
| 20370 |
\begin{align*}
y^{\prime }&=-\frac {\ln \left (x -1\right )-\coth \left (x +1\right ) x^{2}-2 \coth \left (x +1\right ) x y-\coth \left (x +1\right )-\coth \left (x +1\right ) y^{2}}{\ln \left (x -1\right )} \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
4.645 |
|
| 20371 |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.645 |
|
| 20372 |
\begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.645 |
|
| 20373 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+y&=\sin \left (x \right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
✗ |
✓ |
✗ |
✓ |
4.645 |
|
| 20374 |
\begin{align*}
4 y&={y^{\prime }}^{2}+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.647 |
|
| 20375 |
\begin{align*}
x^{4} y^{\prime \prime }&=\left (x^{3}+2 y x \right ) y^{\prime }-4 y^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.647 |
|
| 20376 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 6 & 1\le t <3 \\ 0 & 3\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.647 |
|
| 20377 |
\begin{align*}
-\sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.648 |
|
| 20378 |
\begin{align*}
\theta ^{\prime }&=-a \theta +{\mathrm e}^{b t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.648 |
|
| 20379 |
\begin{align*}
y^{\prime }+4 y x&=8 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.648 |
|
| 20380 |
\begin{align*}
x y^{\prime }&=a \,x^{n} y^{2}+m y-a \,b^{2} x^{n +2 m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.649 |
|
| 20381 |
\begin{align*}
x^{\prime }&=\cos \left (\frac {x}{t}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.649 |
|
| 20382 |
\begin{align*}
y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.651 |
|
| 20383 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.651 |
|
| 20384 |
\begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+4&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.652 |
|
| 20385 |
\begin{align*}
y^{\prime }&=\tan \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.652 |
|
| 20386 |
\begin{align*}
x \ln \left (x \right ) y^{\prime }-y&=x^{3} \left (3 \ln \left (x \right )-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.652 |
|
| 20387 |
\begin{align*}
y^{\prime \prime }&=\frac {3 k y^{2}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.654 |
|
| 20388 |
\begin{align*}
y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.654 |
|
| 20389 |
\begin{align*}
y^{\prime }&=x -y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.655 |
|
| 20390 |
\begin{align*}
x -y+\left (y-x +2\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.655 |
|
| 20391 |
\begin{align*}
x^{2} y^{\prime }-y^{2}-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.656 |
|
| 20392 |
\begin{align*}
y^{\prime }&=-\frac {2 a}{-y-2 a -2 y^{4} a +16 a^{2} x y^{2}-32 a^{3} x^{2}-2 y^{6} a +24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.656 |
|
| 20393 |
\begin{align*}
x^{3} y^{\prime }&=x^{4}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.657 |
|
| 20394 |
\begin{align*}
\cos \left (t \right ) y+y^{\prime }&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.658 |
|
| 20395 |
\begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.659 |
|
| 20396 |
\begin{align*}
x y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.661 |
|
| 20397 |
\begin{align*}
x^{2} y+4 y x +2 y+\left (x^{2}+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.662 |
|
| 20398 |
\begin{align*}
x^{2} y^{\prime }&=1-x^{2}+y^{2}-x^{2} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.664 |
|
| 20399 |
\begin{align*}
\left (-2 y+1\right ) {y^{\prime }}^{2}+\left (1+y^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.664 |
|
| 20400 |
\begin{align*}
2 x +y y^{\prime } \left (4 {y^{\prime }}^{2}+6\right )&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
4.664 |
|