| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 22301 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=2 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.055 |
|
| 22302 |
\begin{align*}
y \sin \left (x \right )^{2}-\left (\cot \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.056 |
|
| 22303 |
\begin{align*}
x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.057 |
|
| 22304 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.064 |
|
| 22305 |
\begin{align*}
y^{\prime } x -y+x \sec \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.065 |
|
| 22306 |
\begin{align*}
4 y+3 \left (2 x -1\right ) \left (y^{\prime }+y^{4}\right )&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.071 |
|
| 22307 |
\begin{align*}
y^{\prime }&=\frac {-x +3}{y+5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.077 |
|
| 22308 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.088 |
|
| 22309 |
\begin{align*}
\left (x^{2}-2 x -8\right ) y^{\prime }&=y^{2}+y-2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.088 |
|
| 22310 |
\begin{align*}
y^{m} x^{n} \left (a x y^{\prime }+b y\right )+\alpha x y^{\prime }+\beta y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.089 |
|
| 22311 |
\begin{align*}
\left (x +y+2\right ) y^{\prime }&=-x -y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.091 |
|
| 22312 |
\begin{align*}
1&=y^{\prime } \cos \left (y\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
10.093 |
|
| 22313 |
\begin{align*}
x^{\prime }&=k \left (A -n x\right ) \left (M -m x\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.093 |
|
| 22314 |
\begin{align*}
y^{\prime }&=\frac {150 x^{3}+125 \sqrt {x}+125+125 y^{2}-100 x^{3} y-500 \sqrt {x}\, y+20 x^{6}+200 x^{{7}/{2}}+500 x +125 y^{3}-150 x^{3} y^{2}-750 y^{2} \sqrt {x}+60 x^{6} y+600 y x^{{7}/{2}}+1500 y x -8 x^{9}-120 x^{{13}/{2}}-600 x^{4}-1000 x^{{3}/{2}}}{125 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.094 |
|
| 22315 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}&=-x^{9} y^{5} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.094 |
|
| 22316 |
\begin{align*}
y x -x&=\left (x y^{2}+x -y^{2}-1\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.096 |
|
| 22317 |
\begin{align*}
v+\left (2 x +1-v x \right ) v^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.098 |
|
| 22318 |
\begin{align*}
y^{\prime } \ln \left (y^{\prime }\right )-\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.112 |
|
| 22319 |
\begin{align*}
\left (3+2 x +4 y\right ) y^{\prime }&=x +2 y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.113 |
|
| 22320 |
\begin{align*}
y^{\prime } x&=6 y+12 x^{4} y^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.115 |
|
| 22321 |
\begin{align*}
y^{2}+y x +1+\left (x^{2}+y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.115 |
|
| 22322 |
\begin{align*}
\left (5+2 x -4 y\right ) y^{\prime }&=x -2 y+3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.119 |
|
| 22323 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\cosh \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.122 |
|
| 22324 |
\begin{align*}
b y+a \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
10.124 |
|
| 22325 |
\begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.132 |
|
| 22326 |
\begin{align*}
2 y-3 t +y^{\prime } t&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.139 |
|
| 22327 |
\begin{align*}
4+\left (x -y+2\right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.140 |
|
| 22328 |
\begin{align*}
y \left (2 x^{2}-y x +1\right )+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.146 |
|
| 22329 |
\begin{align*}
y^{\prime } x&=a \,x^{2 n} {\mathrm e}^{\lambda x} y^{2}+\left (b \,x^{n} {\mathrm e}^{\lambda x}-n \right ) y+c \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.151 |
|
| 22330 |
\begin{align*}
y^{\prime }&=x y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.154 |
|
| 22331 |
\begin{align*}
x^{2} \left (1-y\right ) y^{\prime }+\left (x +1\right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.155 |
|
| 22332 |
\begin{align*}
y^{\prime }-y x&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.164 |
|
| 22333 |
\begin{align*}
y+y^{\prime } x +\frac {y^{3} \left (-y^{\prime } x +y\right )}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.169 |
|
| 22334 |
\begin{align*}
x -y \ln \left (y\right )+y \ln \left (x \right )+x \left (\ln \left (y\right )-\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.185 |
|
| 22335 |
\begin{align*}
y^{\prime }&=\frac {x +3 y}{x -y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.186 |
|
| 22336 |
\begin{align*}
y&=2 y^{\prime }+\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.191 |
|
| 22337 |
\begin{align*}
3 y y^{\prime \prime }&=36 y^{2}+2 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.192 |
|
| 22338 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.197 |
|
| 22339 |
\begin{align*}
y^{\prime }&=x y^{2}-\frac {2 y}{x}-\frac {1}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.205 |
|
| 22340 |
\begin{align*}
y^{\prime }&=y^{2}+a x \tan \left (b x \right )^{m} y+a \tan \left (b x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.205 |
|
| 22341 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -x^{4}+y^{2} \left (-x^{2}+1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.209 |
|
| 22342 |
\begin{align*}
\sin \left (y\right ) y+x \left (\sin \left (y\right )-y \cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.211 |
|
| 22343 |
\begin{align*}
x +y+\left (2 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.213 |
|
| 22344 |
\begin{align*}
2 x -6 y+3-\left (1+x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.221 |
|
| 22345 |
\begin{align*}
y^{3} y^{\prime }+y^{4} x&=x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.224 |
|
| 22346 |
\begin{align*}
y \left (x^{4}-y^{2}\right )+x \left (x^{4}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.225 |
|
| 22347 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\arctan \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.229 |
|
| 22348 |
\begin{align*}
\left (-x +y\right ) y^{\prime }&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.233 |
|
| 22349 |
\begin{align*}
y^{\prime }&=x y^{3} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.237 |
|
| 22350 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=-2 x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.249 |
|
| 22351 |
\begin{align*}
\left (3+2 \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime }&=1+2 \sin \left (y\right )+\cos \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.255 |
|
| 22352 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +y&=\frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.257 |
|
| 22353 |
\begin{align*}
2 x +3 y+\left (3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.261 |
|
| 22354 |
\begin{align*}
{y^{\prime }}^{2}&=\left (-1+y\right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.266 |
|
| 22355 |
\begin{align*}
y&=\sin \left (y^{\prime }\right )-y^{\prime } \cos \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.267 |
|
| 22356 |
\begin{align*}
y^{\prime }&=\sqrt {x -y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.270 |
|
| 22357 |
\begin{align*}
2 x +y-\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.273 |
|
| 22358 |
\begin{align*}
y^{\prime }&=-y^{2} {\mathrm e}^{-t^{2}} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.274 |
|
| 22359 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\lambda x} f \left (x \right ) y^{2}+\left (a f \left (x \right )-\lambda \right ) y+b \,{\mathrm e}^{-\lambda x} f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.286 |
|
| 22360 |
\begin{align*}
{y^{\prime }}^{2}-\left (4 y+1\right ) y^{\prime }+\left (4 y+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.290 |
|
| 22361 |
\begin{align*}
y^{\prime }&=\frac {y^{2} \left (2+F \left (\frac {x^{2}-y}{y x^{2}}\right ) x^{2}\right )}{x^{3}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
10.293 |
|
| 22362 |
\begin{align*}
\left (t +3\right ) \cos \left (y+t \right )+\sin \left (y+t \right )+\left (t +3\right ) \cos \left (y+t \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.295 |
|
| 22363 |
\begin{align*}
y^{\prime } x&=x \tan \left (\frac {y}{x}\right )+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.306 |
|
| 22364 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.306 |
|
| 22365 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}}-\frac {y}{x}-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.309 |
|
| 22366 |
\begin{align*}
\frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
10.313 |
|
| 22367 |
\begin{align*}
1-x^{2} y+x^{2} \left (-x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.314 |
|
| 22368 |
\begin{align*}
y^{\prime } \sqrt {x^{3}+1}&=x^{2} y+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.316 |
|
| 22369 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +8 \left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
10.328 |
|
| 22370 |
\begin{align*}
y^{\prime }+b^{2} y^{2}&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.329 |
|
| 22371 |
\begin{align*}
y^{\prime }+\sqrt {\frac {1-y^{2}}{-x^{2}+1}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.332 |
|
| 22372 |
\begin{align*}
\sin \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x^{2}}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.339 |
|
| 22373 |
\begin{align*}
x^{2} \left (x +y\right ) y^{\prime \prime }-\left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
10.340 |
|
| 22374 |
\begin{align*}
y^{\prime } x&=y+x \cos \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.343 |
|
| 22375 |
\begin{align*}
y^{\prime }&=-y^{3}+\frac {y^{2}}{\left (a x +b \right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
10.346 |
|
| 22376 |
\begin{align*}
\frac {2}{\sqrt {-x^{2}+1}}+y \cos \left (y x \right )+\left (x \cos \left (y x \right )-\frac {1}{y^{{1}/{3}}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
10.348 |
|
| 22377 |
\begin{align*}
2 y y^{\prime } x&=y^{2}-2 x^{3} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.348 |
|
| 22378 |
\begin{align*}
y^{\prime }&=\frac {2+y}{2 t +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.350 |
|
| 22379 |
\begin{align*}
L y^{\prime }+R y&=E \,{\mathrm e}^{i \omega x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.352 |
|
| 22380 |
\begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.355 |
|
| 22381 |
\begin{align*}
4 x -y+\left (6 y-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.358 |
|
| 22382 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
10.359 |
|
| 22383 |
\begin{align*}
x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.362 |
|
| 22384 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.363 |
|
| 22385 |
\begin{align*}
\cos \left (x \right ) \cos \left (y\right )+2 x -\left (\sin \left (x \right ) \sin \left (y\right )+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.379 |
|
| 22386 |
\begin{align*}
y^{\prime } x +\left (1-a y \ln \left (x \right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.382 |
|
| 22387 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda \operatorname {arccot}\left (x \right )^{n} y-a^{2}+a \lambda \operatorname {arccot}\left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.384 |
|
| 22388 |
\begin{align*}
3 x^{2} y y^{\prime }+1+2 x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.387 |
|
| 22389 |
\begin{align*}
a \left (1+k \right ) x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
10.387 |
|
| 22390 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+8 y&=\left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
10.388 |
|
| 22391 |
\begin{align*}
x \left (1-2 x^{2} y\right ) y^{\prime }+y&=3 y^{2} x^{2} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.391 |
|
| 22392 |
\begin{align*}
\sqrt {y}+\left (x +1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.396 |
|
| 22393 |
\begin{align*}
1-y^{2} \cos \left (t y\right )+\left (t y \cos \left (t y\right )+\sin \left (t y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
10.402 |
|
| 22394 |
\begin{align*}
y^{\prime }&=y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.408 |
|
| 22395 |
\begin{align*}
2 x +y+1+\left (4 x +2 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.409 |
|
| 22396 |
\begin{align*}
x^{\prime \prime }-p \left (t \right ) x&=q \left (t \right ) \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
10.412 |
|
| 22397 |
\begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.413 |
|
| 22398 |
\begin{align*}
y y^{\prime }&=a x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.414 |
|
| 22399 |
\begin{align*}
y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.429 |
|
| 22400 |
\begin{align*}
y^{\prime \prime }-x^{3} y^{\prime }-y x -x^{3}-x^{2}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
10.431 |
|