| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 18301 |
\begin{align*}
y^{\prime }&=y^{2}-a^{2} x^{2}+3 a \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.226 |
|
| 18302 |
\begin{align*}
f \left (x \right )^{2} y^{\prime \prime }&=3 f \left (x \right )^{3}-a f \left (x \right )^{5}-f \left (x \right )^{2} y+3 f \left (x \right ) f^{\prime }\left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.227 |
|
| 18303 |
\begin{align*}
4 x^{2} y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.229 |
|
| 18304 |
\begin{align*}
y^{\prime }&=2 y^{3}+t^{2} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3.229 |
|
| 18305 |
\begin{align*}
2 x +\frac {x^{2}+y^{2}}{x^{2} y}&=\frac {\left (x^{2}+y^{2}\right ) y^{\prime }}{x y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.229 |
|
| 18306 |
\begin{align*}
y^{\prime }&=4 y-5 \\
y \left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.230 |
|
| 18307 |
\begin{align*}
y&=x y^{\prime }+\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.230 |
|
| 18308 |
\begin{align*}
y^{\prime \prime }&=-9 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.230 |
|
| 18309 |
\begin{align*}
t^{2} y+y^{\prime }&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.231 |
|
| 18310 |
\begin{align*}
y^{\prime \prime }+\left (1-\frac {3}{4 x^{2}}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.231 |
|
| 18311 |
\begin{align*}
\left (x -{\mathrm e}^{x}\right ) y^{\prime }+x \,{\mathrm e}^{x}+\left (1-{\mathrm e}^{x}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.231 |
|
| 18312 |
\begin{align*}
2 {y^{\prime }}^{2}+x y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.231 |
|
| 18313 |
\begin{align*}
y^{\prime }-7 y&=\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.232 |
|
| 18314 |
\begin{align*}
y^{\prime }&=\left (t +1\right ) \left (1+y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.233 |
|
| 18315 |
\begin{align*}
y^{\prime }+y \sin \left (x \right )&=\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.233 |
|
| 18316 |
\begin{align*}
x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.233 |
|
| 18317 |
\begin{align*}
y^{\prime \prime }-\tan \left (x \right ) y^{\prime }-\frac {\tan \left (x \right ) y}{x}&=\frac {y^{3}}{x^{3}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3.233 |
|
| 18318 |
\begin{align*}
y^{\left (8\right )}+8 y^{\left (7\right )}+28 y^{\left (6\right )}+56 y^{\left (5\right )}+70 y^{\prime \prime \prime \prime }+56 y^{\prime \prime \prime }+28 y^{\prime \prime }+8 y^{\prime }&={\mathrm e}^{-x} x^{9} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.233 |
|
| 18319 |
\begin{align*}
2 y y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.234 |
|
| 18320 |
\begin{align*}
y^{\prime }&=x^{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.234 |
|
| 18321 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.234 |
|
| 18322 |
\begin{align*}
x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.234 |
|
| 18323 |
\begin{align*}
y^{\prime }&=\frac {F \left (-\frac {-1+y \ln \left (x \right )}{y}\right ) y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.235 |
|
| 18324 |
\begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\sin \left (x \right ) \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.236 |
|
| 18325 |
\begin{align*}
x^{\prime }&=-3 x+y-3 z+2 \,{\mathrm e}^{t} \\
y^{\prime }&=4 x-y+2 z+4 \,{\mathrm e}^{t} \\
z^{\prime }&=4 x-2 y+3 z+4 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.236 |
|
| 18326 |
\begin{align*}
y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| 18327 |
\begin{align*}
x^{3} y^{4}+x +\left (x^{4} y^{3}+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.237 |
|
| 18328 |
\begin{align*}
x^{3}+\left (y+1\right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| 18329 |
\begin{align*}
y^{\prime }&=2 t y^{2}+3 y^{2} t^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| 18330 |
\begin{align*}
a {y^{\prime }}^{3}&=27 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| 18331 |
\begin{align*}
2 y x +x^{2}+x^{4}-\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| 18332 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\left (y-t \right )^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.238 |
|
| 18333 |
\begin{align*}
y^{\prime }-7 y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.238 |
|
| 18334 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x -4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.239 |
|
| 18335 |
\begin{align*}
y^{\prime }&=\sin \left (y\right )-\cos \left (x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3.239 |
|
| 18336 |
\begin{align*}
x y^{\prime }+3 y&=2 x^{5} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.240 |
|
| 18337 |
\begin{align*}
\ln \left (t \right ) y+\left (-3+t \right ) y^{\prime }&=2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.240 |
|
| 18338 |
\begin{align*}
y^{\prime }-\frac {y}{3}&=3 \cos \left (t \right ) \\
y \left (0\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.240 |
|
| 18339 |
\begin{align*}
y^{\prime }&=\frac {2 x^{3} y+x^{6}+x^{2} y^{2}+y^{3}}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.242 |
|
| 18340 |
\begin{align*}
y^{\prime }&=\frac {x}{y}-\frac {x}{y+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.242 |
|
| 18341 |
\begin{align*}
4 x^{2} y^{\prime \prime }+8 x y^{\prime }+\left (2 x -3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.242 |
|
| 18342 |
\begin{align*}
\sin \left (x \right ) y^{\prime }&=\ln \left (y\right ) y \\
y \left (\frac {\pi }{3}\right ) &= {\mathrm e} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.243 |
|
| 18343 |
\begin{align*}
y^{\prime }+y \sec \left (t \right )&=t \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.243 |
|
| 18344 |
\begin{align*}
y^{\prime }&=1+x +y+y x \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.244 |
|
| 18345 |
\begin{align*}
y^{\prime \prime }&=f \left (x \right ) y^{2}-y^{3}+\left (f \left (x \right )-3 y\right ) y^{\prime } \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
3.244 |
|
| 18346 |
\begin{align*}
y^{\prime }&=\frac {-3 x^{2} y+1+x^{6} y^{2}+y^{3} x^{9}}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.244 |
|
| 18347 |
\begin{align*}
p^{\prime }&=\frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.244 |
|
| 18348 |
\begin{align*}
y^{\prime }&=\cos \left (x -y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.245 |
|
| 18349 |
\begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y \left (L \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.246 |
|
| 18350 |
\begin{align*}
\left (t +1\right ) y+t y^{\prime }&=t \\
y \left (\ln \left (2\right )\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.246 |
|
| 18351 |
\begin{align*}
i^{\prime }+5 i&=10 \\
i \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.246 |
|
| 18352 |
\begin{align*}
2 y^{2}+y \,{\mathrm e}^{y x}+\left (4 y x +x \,{\mathrm e}^{y x}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.246 |
|
| 18353 |
\begin{align*}
3 x y^{\prime }+y&=12 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.247 |
|
| 18354 |
\begin{align*}
y^{\prime }&=\frac {1-2 x}{y} \\
y \left (1\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.247 |
|
| 18355 |
\begin{align*}
y^{2}+1-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.247 |
|
| 18356 |
\begin{align*}
3 y+x^{4} y^{\prime }&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.248 |
|
| 18357 |
\begin{align*}
\left (t^{2}+1\right ) y^{\prime }&=y t -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.249 |
|
| 18358 |
\begin{align*}
t y^{\prime }&=y-2 y t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.249 |
|
| 18359 |
\begin{align*}
y^{\prime }&=\sqrt {x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.250 |
|
| 18360 |
\begin{align*}
y^{\prime }&=y+y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.250 |
|
| 18361 |
\begin{align*}
-x y^{\prime }+y&=3-2 x^{2} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.250 |
|
| 18362 |
\begin{align*}
y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 \csc \left (x \right )^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.250 |
|
| 18363 |
\begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.250 |
|
| 18364 |
\begin{align*}
2 x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2}-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.251 |
|
| 18365 |
\begin{align*}
y^{\prime }&=y^{2} {\mathrm e}^{-x}+4 y+2 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.252 |
|
| 18366 |
\begin{align*}
y^{\prime }+a y&=\sqrt {t +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.252 |
|
| 18367 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-\left (2 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.252 |
|
| 18368 |
\begin{align*}
y^{\prime }-4 y&=\cos \left (3 t \right )+\sin \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.252 |
|
| 18369 |
\begin{align*}
2 x y^{\prime }-y&=2 x \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.253 |
|
| 18370 |
\begin{align*}
x y^{2} y^{\prime }&=y+1 \\
y \left (3 \,{\mathrm e}^{2}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.253 |
|
| 18371 |
\begin{align*}
x^{3} \left (y^{\prime }-x \right )&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.253 |
|
| 18372 |
\begin{align*}
\left (x +2\right ) y^{\prime }+y&=\left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right . \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.254 |
|
| 18373 |
\begin{align*}
y^{\prime }-9 y&=90 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.254 |
|
| 18374 |
\begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.254 |
|
| 18375 |
\begin{align*}
x y^{\prime }+\left (x +1\right ) y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.255 |
|
| 18376 |
\begin{align*}
2 y-y x -3+x y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.256 |
|
| 18377 |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.256 |
|
| 18378 |
\begin{align*}
2 x^{2}+1&=\left (y^{5}-1\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.256 |
|
| 18379 |
\begin{align*}
\frac {2 x}{y}+5 y^{2}-4 x +\left (3 y^{2}-\frac {x^{2}}{y^{2}}+10 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.256 |
|
| 18380 |
\begin{align*}
4 x^{2} y^{\prime \prime }+2 x \left (x^{2}+8\right ) y^{\prime }+\left (3 x^{2}+5\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.257 |
|
| 18381 |
\begin{align*}
-y-3 x y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.257 |
|
| 18382 |
\begin{align*}
y^{\prime }&=\frac {-x y^{2}+x^{3}-x -y^{6}+3 x^{2} y^{4}-3 y^{2} x^{4}+x^{6}}{\left (x^{2}-y^{2}-1\right ) y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.257 |
|
| 18383 |
\begin{align*}
x^{\prime \prime }+k^{2} x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= v_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.257 |
|
| 18384 |
\begin{align*}
y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right )+\frac {18 x -8}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.257 |
|
| 18385 |
\begin{align*}
y^{\prime }-y x&={\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.258 |
|
| 18386 |
\begin{align*}
y^{\prime }&=\frac {4 y^{2}}{x^{2}}-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.259 |
|
| 18387 |
\begin{align*}
x y^{2} y^{\prime }-y^{3}&=\frac {x^{4}}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.259 |
|
| 18388 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&={y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.260 |
|
| 18389 |
\begin{align*}
\left (x^{2}+1\right ) y y^{\prime }+4&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.260 |
|
| 18390 |
\begin{align*}
x^{2} y^{\prime }+2 x \left (1-x \right ) y&={\mathrm e}^{x} \left (2 \,{\mathrm e}^{x}-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.261 |
|
| 18391 |
\begin{align*}
y^{\prime }&=\frac {1}{x +y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.261 |
|
| 18392 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=\sqrt {x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.263 |
|
| 18393 |
\begin{align*}
x^{\prime }&=\frac {3 x t^{2}}{-t^{3}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.263 |
|
| 18394 |
\begin{align*}
\left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.263 |
|
| 18395 |
\begin{align*}
x y \left (x y^{\prime }-y\right )^{2}+2 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.263 |
|
| 18396 |
\begin{align*}
y y^{\prime }&=x \left (1+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.264 |
|
| 18397 |
\begin{align*}
y^{\prime }+\frac {y}{x}&={\mathrm e}^{y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.264 |
|
| 18398 |
\begin{align*}
{y^{\prime }}^{2}-x y \left (x^{2}+y^{2}\right ) y^{\prime }+x^{4} y^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.264 |
|
| 18399 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\sin \left (x \right )}+\cos \left (x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.265 |
|
| 18400 |
\begin{align*}
r^{\prime }&=-2 r t \\
r \left (0\right ) &= r_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.265 |
|