| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 23401 |
\begin{align*}
y^{\prime }&=-\frac {t}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.188 |
|
| 23402 |
\begin{align*}
y^{\prime \prime \prime }-a^{2} \left ({y^{\prime }}^{5}+2 {y^{\prime }}^{3}+y^{\prime }\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.188 |
|
| 23403 |
\begin{align*}
x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.191 |
|
| 23404 |
\begin{align*}
y^{\prime }&=\sin \left (y\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.194 |
|
| 23405 |
\begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.198 |
|
| 23406 |
\begin{align*}
y^{\prime } x&=x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.198 |
|
| 23407 |
\begin{align*}
y^{\prime }&=-x +\sqrt {x^{2}+2 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.200 |
|
| 23408 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.204 |
|
| 23409 |
\begin{align*}
3 x^{2} y^{\prime }+2 x^{2}-3 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.210 |
|
| 23410 |
\begin{align*}
\left (t -\sqrt {t y}\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.221 |
|
| 23411 |
\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. |
✓ |
✓ |
✓ |
✓ |
8.222 |
|
| 23412 |
\begin{align*}
4 y y^{\prime \prime }-3 {y^{\prime }}^{2}-12 y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.231 |
|
| 23413 |
\begin{align*}
y^{\prime }&=3 y^{{2}/{3}}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.235 |
|
| 23414 |
\begin{align*}
y^{\prime }&=-\frac {1}{-\left (y^{3}\right )^{{2}/{3}} x -\textit {\_F1} \left (y^{3}-3 \ln \left (x \right )\right ) \left (y^{3}\right )^{{1}/{3}} x} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
8.236 |
|
| 23415 |
\begin{align*}
w^{\prime }&=\left (1-w\right ) \sin \left (w\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.240 |
|
| 23416 |
\begin{align*}
y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.241 |
|
| 23417 |
\begin{align*}
\frac {2 y y^{\prime } x}{3}&=\sqrt {x^{6}-y^{4}}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.243 |
|
| 23418 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (-a \cos \left (x \right )^{2} \sin \left (x \right )^{2}-m \left (m -1\right ) \sin \left (x \right )^{2}-n \left (n -1\right ) \cos \left (x \right )^{2}\right ) y}{\cos \left (x \right )^{2} \sin \left (x \right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.244 |
|
| 23419 |
\begin{align*}
t^{2} y^{\prime \prime }+3 y^{\prime } t -4 y&=t^{4} \\
y \left (-1\right ) &= y_{1} \\
y^{\prime }\left (-1\right ) &= y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.250 |
|
| 23420 |
\begin{align*}
a \left (1+k \right ) x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
8.251 |
|
| 23421 |
\begin{align*}
\left (\operatorname {a1} +\operatorname {b1} \,x^{k}+\operatorname {c1} \,x^{2 k}\right ) y+x \left (\operatorname {a0} +\operatorname {b0} \,x^{k}\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.253 |
|
| 23422 |
\begin{align*}
2 x^{2} y y^{\prime }+y^{2}&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.253 |
|
| 23423 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (x^{2}+1\right )-y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.255 |
|
| 23424 |
\begin{align*}
{y^{\prime }}^{3}-a x y^{\prime }+x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.256 |
|
| 23425 |
\begin{align*}
1&=b \left (\cos \left (y\right )+x \sin \left (y\right ) y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.256 |
|
| 23426 |
\begin{align*}
y y^{\prime } x&=x^{2}+3 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.257 |
|
| 23427 |
\begin{align*}
y^{\prime }&=-\left (-\frac {\ln \left (y\right )}{x}+\frac {\ln \left (y\right )}{x \ln \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.257 |
|
| 23428 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.257 |
|
| 23429 |
\begin{align*}
y^{\prime } x +y&=x^{4} y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.263 |
|
| 23430 |
\begin{align*}
y+\left (4 x -y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.270 |
|
| 23431 |
\begin{align*}
\left (x +2 y+1\right ) y^{\prime }+1-x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.271 |
|
| 23432 |
\begin{align*}
y^{\prime }&=\frac {-32 y x -8 x^{3}-16 a \,x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}+96 a x y^{2}+12 x^{4} y+48 y a \,x^{3}+48 y a^{2} x^{2}+x^{6}+6 x^{5} a +12 a^{2} x^{4}+8 a^{3} x^{3}}{64 y+16 x^{2}+32 a x +64} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.273 |
|
| 23433 |
\begin{align*}
\left (2+3 x -y x \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.273 |
|
| 23434 |
\begin{align*}
2 y^{\prime \prime } x -\left (x -1\right ) y^{\prime }+a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.280 |
|
| 23435 |
\begin{align*}
2 y-4 \left (1-x \right ) y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime }&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.283 |
|
| 23436 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {2}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.290 |
|
| 23437 |
\begin{align*}
y y^{\prime } x&=a \,x^{n}+b y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.294 |
|
| 23438 |
\begin{align*}
y^{\prime }&=x \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.294 |
|
| 23439 |
\begin{align*}
2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y&=1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.295 |
|
| 23440 |
\begin{align*}
\left (x +2 y\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.303 |
|
| 23441 |
\begin{align*}
y^{\prime }&=-\frac {2}{t}+\frac {y}{t}+\frac {y^{2}}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.305 |
|
| 23442 |
\begin{align*}
y^{\prime } x +x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.310 |
|
| 23443 |
\begin{align*}
\left (a +b \cosh \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.311 |
|
| 23444 |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.311 |
|
| 23445 |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{y^{2}+y^{{3}/{2}}+\sqrt {y}\, x^{2}-2 y^{{3}/{2}} x +y^{{5}/{2}}+x^{3}-3 x^{2} y+3 x y^{2}-y^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.319 |
|
| 23446 |
\begin{align*}
y^{\left (6\right )}+y-\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.319 |
|
| 23447 |
\begin{align*}
y^{\prime } x -y \left (\ln \left (y x \right )-1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.323 |
|
| 23448 |
\begin{align*}
y^{\prime }&=t^{2} y^{2}+y^{2}-t^{2}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.323 |
|
| 23449 |
\begin{align*}
\left (1-y^{2} x^{2}\right ) y^{\prime }&=x y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.329 |
|
| 23450 |
\begin{align*}
y y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.332 |
|
| 23451 |
\begin{align*}
y^{\prime }-x y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.338 |
|
| 23452 |
\begin{align*}
y^{\prime }&=-\left (-\frac {\ln \left (y\right )}{x}+\frac {\cos \left (x \right ) \ln \left (y\right )}{\sin \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.338 |
|
| 23453 |
\begin{align*}
b y+\left (a +x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.343 |
|
| 23454 |
\begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.343 |
|
| 23455 |
\begin{align*}
z^{\prime }+z \cos \left (x \right )&=z^{n} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.345 |
|
| 23456 |
\begin{align*}
\operatorname {f3} \left (y\right )+\operatorname {f2} \left (y\right ) y^{\prime }+\operatorname {f1} \left (y\right ) {y^{\prime }}^{2}+\operatorname {f0} \left (y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
8.347 |
|
| 23457 |
\begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2 \left (x -y\right )^{2} \left (x +y\right )^{2}}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2 \left (x -y\right )^{2} \left (x +y\right )^{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.350 |
|
| 23458 |
\begin{align*}
y^{\prime }&=x +\frac {\sec \left (x \right ) y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.352 |
|
| 23459 |
\begin{align*}
x x^{\prime }+t&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.352 |
|
| 23460 |
\begin{align*}
x^{n} y^{\prime \prime }+a x y^{\prime }-\left (b^{2} x^{n}+2 b \,x^{n -1}+a b x +a \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
8.356 |
|
| 23461 |
\begin{align*}
y^{\prime }&=y^{2}+a x \,{\mathrm e}^{\lambda x} y+a \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.358 |
|
| 23462 |
\begin{align*}
2 \left (x^{2}+1\right ) y^{\prime }&=\left (2 y^{2}-1\right ) x y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.359 |
|
| 23463 |
\begin{align*}
y^{\prime \prime }-x^{2} y-x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.362 |
|
| 23464 |
\begin{align*}
y^{\prime }&=\frac {x^{3} y^{3}+6 y^{2} x^{2}+12 y x +8+2 x}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.364 |
|
| 23465 |
\begin{align*}
y y^{\prime \prime }+y&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.371 |
|
| 23466 |
\begin{align*}
2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.376 |
|
| 23467 |
\begin{align*}
x +3 y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.377 |
|
| 23468 |
\begin{align*}
\left (x^{2}-y^{4}\right ) y^{\prime }&=y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.378 |
|
| 23469 |
\begin{align*}
\left (3+2 x +4 y\right ) y^{\prime }-2 y-x -1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.380 |
|
| 23470 |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
8.386 |
|
| 23471 |
\begin{align*}
3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.387 |
|
| 23472 |
\begin{align*}
\left (x -1\right ) \left (y^{2}-y+1\right )&=\left (1+y\right ) \left (x^{2}+x +1\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.388 |
|
| 23473 |
\begin{align*}
{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{4} \left (y-b \right )^{3}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
8.390 |
|
| 23474 |
\begin{align*}
\left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.392 |
|
| 23475 |
\begin{align*}
y^{\prime }&=\frac {y+x^{3} \ln \left (x \right )+x^{4}+x^{3}+7 x y^{2} \ln \left (x \right )+7 y^{2} x^{2}+7 x y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.395 |
|
| 23476 |
\begin{align*}
-a y+\left (c -x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.398 |
|
| 23477 |
\begin{align*}
-y+y^{\prime } x&=x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.408 |
|
| 23478 |
\begin{align*}
y y^{\prime } x +1+y^{2}&=0 \\
y \left (5\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.409 |
|
| 23479 |
\begin{align*}
x^{2} y^{\prime }+x y^{3}+a y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.413 |
|
| 23480 |
\begin{align*}
\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.419 |
|
| 23481 |
\begin{align*}
y^{\prime } x&=y-2 x \tanh \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.420 |
|
| 23482 |
\begin{align*}
3 x y^{2}+2+2 x^{2} y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.421 |
|
| 23483 |
\begin{align*}
1-x^{2} y+x^{2} \left (-x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.422 |
|
| 23484 |
\begin{align*}
y y^{\prime }&=-x \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.423 |
|
| 23485 |
\begin{align*}
y^{\prime }&=\frac {y+x^{3} a \ln \left (x +1\right )+a \,x^{4}+a \,x^{3}-x y^{2} \ln \left (x +1\right )-y^{2} x^{2}-x y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.427 |
|
| 23486 |
\begin{align*}
{y^{\prime }}^{3} y^{\prime \prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.434 |
|
| 23487 |
\begin{align*}
x^{2} y y^{\prime }&=\left (-1+y^{2}\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.437 |
|
| 23488 |
\begin{align*}
{\mathrm e}^{t} y+t \,{\mathrm e}^{t} y+\left ({\mathrm e}^{t} t +2\right ) y^{\prime }&=0 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.437 |
|
| 23489 |
\begin{align*}
y^{\prime }&=\frac {y+t}{t -y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.440 |
|
| 23490 |
\begin{align*}
x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y+\frac {\sqrt {x}\, \left (2+\ln \left (x \right )\right )}{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.448 |
|
| 23491 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{-y^{2}}}{y \left (x^{2}+2 x \right )} \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.453 |
|
| 23492 |
\begin{align*}
t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=4 t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.457 |
|
| 23493 |
\begin{align*}
\left (1-y^{2}\right ) {y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.471 |
|
| 23494 |
\begin{align*}
y^{\prime }&=\frac {-{\mathrm e}^{x} y+y x -x^{3} \ln \left (x \right )-x^{3}-x y^{2} \ln \left (x \right )-x y^{2}}{\left (x -{\mathrm e}^{x}\right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.471 |
|
| 23495 |
\begin{align*}
y \sqrt {x^{2}-1}+x \sqrt {-1+y^{2}}\, y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.472 |
|
| 23496 |
\begin{align*}
{y^{\prime }}^{3}&=a \,x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.475 |
|
| 23497 |
\begin{align*}
{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.477 |
|
| 23498 |
\begin{align*}
y^{\prime }&=-\frac {216 y}{-216 y^{4}-252 y^{3}-396 y^{2}-216 y+36 x^{2}-72 y x +60 y^{5}-36 x y^{3}-72 x y^{2}-24 y^{4} x +4 y^{8}+12 y^{7}+33 y^{6}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.485 |
|
| 23499 |
\begin{align*}
y y^{\prime }+b y^{2}&=a \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.487 |
|
| 23500 |
\begin{align*}
y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.490 |
|