| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 19301 |
\begin{align*}
y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.413 |
|
| 19302 |
\begin{align*}
y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.414 |
|
| 19303 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (4 v \left (v +1\right ) \sin \left (x \right )^{2}-\cos \left (x \right )^{2}+2-4 n^{2}\right ) y}{4 \sin \left (x \right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.417 |
|
| 19304 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.420 |
|
| 19305 |
\begin{align*}
x^{\prime }&=1-x^{2} \\
x \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.421 |
|
| 19306 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }-3 y&=\operatorname {Heaviside}\left (x -4\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.421 |
|
| 19307 |
\begin{align*}
{y^{\prime }}^{2} \sin \left (y^{\prime }\right )-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.424 |
|
| 19308 |
\begin{align*}
{y^{\prime }}^{2}+a y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.425 |
|
| 19309 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-3 y y^{\prime } x +x^{3}+2 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.425 |
|
| 19310 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.425 |
|
| 19311 |
\begin{align*}
y^{\prime } x&=x^{m}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.428 |
|
| 19312 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=2 x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.428 |
|
| 19313 |
\begin{align*}
2 x^{2}+5 x y^{2}+\left (5 x^{2} y-2 y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.428 |
|
| 19314 |
\begin{align*}
y^{\prime }&=\frac {y}{1+t}+10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.428 |
|
| 19315 |
\begin{align*}
\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=x \sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.429 |
|
| 19316 |
\begin{align*}
y y^{\prime }&=x +1 \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.430 |
|
| 19317 |
\begin{align*}
2 x +3 y-1-4 \left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.431 |
|
| 19318 |
\begin{align*}
y^{\prime }&=1-t +y^{2}-t y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.432 |
|
| 19319 |
\begin{align*}
y^{\prime }&=\frac {1+2 y}{x \left (-2+y x +2 x y^{2}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.432 |
|
| 19320 |
\begin{align*}
3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.434 |
|
| 19321 |
\begin{align*}
y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.435 |
|
| 19322 |
\begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.435 |
|
| 19323 |
\begin{align*}
t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
4.437 |
|
| 19324 |
\begin{align*}
y&=y^{\prime } x -\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.437 |
|
| 19325 |
\begin{align*}
y^{\prime }&=\frac {x^{2} y-y}{1+y} \\
y \left (3\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.437 |
|
| 19326 |
\begin{align*}
y^{\prime }&=2 \left (x +1\right ) \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.438 |
|
| 19327 |
\begin{align*}
y^{\prime }&=2 t y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.438 |
|
| 19328 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.439 |
|
| 19329 |
\begin{align*}
y^{\prime }+a y&=t^{n} {\mathrm e}^{-a t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.439 |
|
| 19330 |
\begin{align*}
{y^{\prime }}^{2}&=f \left (x \right )^{2} \left (y-a \right ) \left (y-b \right ) \left (y-c \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.440 |
|
| 19331 |
\begin{align*}
4 x {y^{\prime }}^{2}&=\left (a -3 x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.440 |
|
| 19332 |
\begin{align*}
-y^{\prime } x +y&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.440 |
|
| 19333 |
\begin{align*}
{\mathrm e}^{x}-\left ({\mathrm e}^{x}+1\right ) y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.442 |
|
| 19334 |
\begin{align*}
y^{3}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.445 |
|
| 19335 |
\begin{align*}
y&=3 x +a \ln \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.446 |
|
| 19336 |
\begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=a \,x^{3}+\left (-2 x^{2}+1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.447 |
|
| 19337 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+{\mathrm e}^{\lambda x} a c +{\mathrm e}^{\mu x} b \mu \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
4.449 |
|
| 19338 |
\begin{align*}
y^{\prime } x&=x +2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.452 |
|
| 19339 |
\begin{align*}
x -y+2+\left (x -y+3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.455 |
|
| 19340 |
\begin{align*}
y^{\prime }&=\frac {t^{2}}{y+y t^{3}} \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.456 |
|
| 19341 |
\begin{align*}
y^{\prime }&=\frac {2 x^{3} y+x^{6}+y^{2} x^{2}+y^{3}}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.457 |
|
| 19342 |
\begin{align*}
\left (-1+y^{2}\right ) \left (y^{2} a^{2}-1\right ) y^{\prime \prime }+b \sqrt {\left (1-y^{2}\right ) \left (1-y^{2} a^{2}\right )}\, {y^{\prime }}^{2}+\left (1+a^{2}-2 y^{2} a^{2}\right ) y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
4.458 |
|
| 19343 |
\begin{align*}
4 x y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.459 |
|
| 19344 |
\begin{align*}
x {y^{\prime }}^{2}&=\left (a -x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.460 |
|
| 19345 |
\begin{align*}
x^{2} y^{\prime }&=y x +x^{2} {\mathrm e}^{\frac {y}{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.461 |
|
| 19346 |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{3}+\frac {2}{3 x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.462 |
|
| 19347 |
\begin{align*}
y-x y^{2} \ln \left (x \right )+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.462 |
|
| 19348 |
\begin{align*}
y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.462 |
|
| 19349 |
\begin{align*}
y^{\prime \prime }&=-\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (v \left (v +1\right ) \sin \left (x \right )^{2}-n^{2}\right ) y}{\sin \left (x \right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.463 |
|
| 19350 |
\begin{align*}
{y^{\prime }}^{2}-y y^{\prime \prime }&=n \sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
4.463 |
|
| 19351 |
\begin{align*}
y^{\prime }+2 y x&=x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.464 |
|
| 19352 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}-y^{2}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
4.465 |
|
| 19353 |
\begin{align*}
y^{\prime } x -y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.466 |
|
| 19354 |
\begin{align*}
x&=\ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.467 |
|
| 19355 |
\begin{align*}
y^{\prime }&=\frac {x \left (-1+y^{2}\right )}{2 \left (x -2\right ) \left (x -1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.471 |
|
| 19356 |
\begin{align*}
y^{\prime }&=a \left (t \right ) y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.471 |
|
| 19357 |
\begin{align*}
y^{3} y^{\prime \prime }&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.473 |
|
| 19358 |
\begin{align*}
\cos \left (x \right ) y^{\prime }+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.473 |
|
| 19359 |
\begin{align*}
\frac {x}{1+y}&=\frac {y y^{\prime }}{x +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.474 |
|
| 19360 |
\begin{align*}
y^{\prime }&=\frac {a^{2} x +a^{3} x^{3}+a^{3} x^{3} y^{2}+2 y a^{2} x^{2}+a x +a^{3} x^{3} y^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1}{a^{3} x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.474 |
|
| 19361 |
\begin{align*}
3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.474 |
|
| 19362 |
\begin{align*}
y^{\prime }&=\frac {2 y^{2}}{x}+\frac {y}{x}-2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.475 |
|
| 19363 |
\begin{align*}
y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.476 |
|
| 19364 |
\begin{align*}
y^{\prime }&=-\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.476 |
|
| 19365 |
\begin{align*}
y^{2} \left (y y^{\prime }-x \right )+x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.477 |
|
| 19366 |
\begin{align*}
y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.477 |
|
| 19367 |
\begin{align*}
x^{\prime }&=2 t^{3} x-6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.481 |
|
| 19368 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x&=\left (x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.483 |
|
| 19369 |
\begin{align*}
y^{\prime } t&=2 y-t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.486 |
|
| 19370 |
\begin{align*}
y^{\prime \prime }-\left (n \left (n +1\right ) k^{2} \operatorname {JacobiSN}\left (x , k\right )^{2}+b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.487 |
|
| 19371 |
\begin{align*}
\left (x +x^{3} \sin \left (2 y\right )\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.487 |
|
| 19372 |
\begin{align*}
y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x}&=4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.488 |
|
| 19373 |
\begin{align*}
\left (x -6 y\right )^{2} y^{\prime }+a +2 y x -6 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.489 |
|
| 19374 |
\begin{align*}
y^{\prime \prime }-2 \left (r +\beta \right ) y^{\prime }+r^{2} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.490 |
|
| 19375 |
\begin{align*}
\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}&=b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.494 |
|
| 19376 |
\begin{align*}
y+y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.494 |
|
| 19377 |
\begin{align*}
x^{2} y^{\prime }+2+a x \left (-y x +1\right )-y^{2} x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.495 |
|
| 19378 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x +a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.495 |
|
| 19379 |
\begin{align*}
3 y y^{\prime \prime }+y&=5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.496 |
|
| 19380 |
\begin{align*}
y^{\prime }&=a +b \,{\mathrm e}^{k x}+c y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.497 |
|
| 19381 |
\begin{align*}
y^{\prime }&=y^{2} {\mathrm e}^{-x}+y-{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.497 |
|
| 19382 |
\begin{align*}
y^{\prime }&=x^{2} {\mathrm e}^{-4 x}-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.497 |
|
| 19383 |
\begin{align*}
y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-\frac {4 x}{3}}+y^{3} {\mathrm e}^{-2 x}\right ) {\mathrm e}^{\frac {2 x}{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.497 |
|
| 19384 |
\begin{align*}
y^{\prime }&=-\frac {y}{1+t}+t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.498 |
|
| 19385 |
\begin{align*}
y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.499 |
|
| 19386 |
\begin{align*}
y^{\prime }+y x&=3 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.501 |
|
| 19387 |
\begin{align*}
2 y y^{\prime \prime }&=y^{2} \left (1-3 y^{2}\right )+6 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.502 |
|
| 19388 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (2 n +1\right ) \cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\left (v +n +1\right ) \left (v -n \right ) y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.502 |
|
| 19389 |
\begin{align*}
y^{\prime }&=\frac {3 t^{2}+4 t +2}{-2+2 y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.503 |
|
| 19390 |
\begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (y x \right )-1\right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.503 |
|
| 19391 |
\begin{align*}
y^{\prime }&=\sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.503 |
|
| 19392 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.505 |
|
| 19393 |
\begin{align*}
y^{\prime }&=\frac {x y^{2}+x}{4 y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.506 |
|
| 19394 |
\begin{align*}
3 y^{2} y^{\prime }&=1+x +a y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.507 |
|
| 19395 |
\begin{align*}
x^{7} y^{2} {y^{\prime }}^{3}-\left (3 x^{6} y^{3}-1\right ) {y^{\prime }}^{2}+3 x^{5} y^{4} y^{\prime }-x^{4} y^{5}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.507 |
|
| 19396 |
\begin{align*}
y+y^{\prime }&=t y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.507 |
|
| 19397 |
\begin{align*}
50 x \left (x -1\right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.508 |
|
| 19398 |
\begin{align*}
\left (a +x \right ) y+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.509 |
|
| 19399 |
\begin{align*}
y^{\prime }&=\frac {-x +1-2 y+3 x^{2}-2 x^{2} y+2 x^{4}+x^{3}-2 x^{3} y+2 x^{5}}{x^{2}-y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.510 |
|
| 19400 |
\begin{align*}
{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.512 |
|