| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 22301 |
\begin{align*}
y^{\prime } x&=\sqrt {1-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.065 |
|
| 22302 |
\begin{align*}
y^{\prime } x +y&=2 x \\
y \left (x_{0} \right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.065 |
|
| 22303 |
\begin{align*}
y^{\prime }&=\frac {x^{4}}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.079 |
|
| 22304 |
\begin{align*}
y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
9.080 |
|
| 22305 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (\left (1+a \right ) x +b \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.081 |
|
| 22306 |
\begin{align*}
y^{\prime }+\sqrt {\frac {1-y^{2}}{-x^{2}+1}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.088 |
|
| 22307 |
\begin{align*}
y^{\prime }&=\frac {y+x^{3} b \ln \left (\frac {1}{x}\right )+b \,x^{4}+b \,x^{3}+x a y^{2} \ln \left (\frac {1}{x}\right )+a \,x^{2} y^{2}+a x y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.098 |
|
| 22308 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+n \left (n -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
9.099 |
|
| 22309 |
\begin{align*}
y^{\prime }&=\frac {-32 a x y-8 a^{2} x^{3}-16 a b \,x^{2}-32 a x +64 y^{3}+48 a \,x^{2} y^{2}+96 b x y^{2}+12 a^{2} x^{4} y+48 y a \,x^{3} b +48 b^{2} x^{2} y+a^{3} x^{6}+6 a^{2} x^{5} b +12 b^{2} x^{4} a +8 b^{3} x^{3}}{64 y+16 a \,x^{2}+32 b x +64} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.102 |
|
| 22310 |
\begin{align*}
y^{2} \left (y^{\prime } x +y\right ) \sqrt {x^{4}+1}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.103 |
|
| 22311 |
\begin{align*}
y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.106 |
|
| 22312 |
\begin{align*}
\left (a +x \right ) y^{\prime }&=b +c y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.106 |
|
| 22313 |
\begin{align*}
y^{\prime }&=\frac {x^{3}+x^{2}+2 \sqrt {x^{3}-6 y}}{2 x +2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.108 |
|
| 22314 |
\begin{align*}
y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.110 |
|
| 22315 |
\begin{align*}
2 y y^{\prime } x&=4 x^{2} \left (2 x +1\right )+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.111 |
|
| 22316 |
\begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }-k^{2} \cos \left (x \right )^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.112 |
|
| 22317 |
\begin{align*}
x^{2} y^{\prime }&=a +b y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.113 |
|
| 22318 |
\begin{align*}
\left (y y^{\prime }+x n \right )^{2}&=\left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
9.113 |
|
| 22319 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-n \left (n +1\right ) y+\frac {\left (n +1\right ) \operatorname {LegendreP}\left (n +1, x\right )-\left (n +1\right ) x \operatorname {LegendreP}\left (n , x\right )}{x^{2}-1}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.120 |
|
| 22320 |
\begin{align*}
y^{\prime } x&=a \,{\mathrm e}^{\lambda x} y^{2}+k y+a \,b^{2} x^{2 k} {\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.122 |
|
| 22321 |
\begin{align*}
y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.125 |
|
| 22322 |
\begin{align*}
\left (-2 y x +x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.127 |
|
| 22323 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.130 |
|
| 22324 |
\begin{align*}
y^{\prime } x&=1+x +a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.131 |
|
| 22325 |
\begin{align*}
4 x^{2} y^{2} y^{\prime }-3 x y^{3}&=x^{2} y^{3}+2 x^{2} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.135 |
|
| 22326 |
\begin{align*}
x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.140 |
|
| 22327 |
\begin{align*}
y^{\prime \prime }&=a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.142 |
|
| 22328 |
\begin{align*}
x^{\prime }+5 x&=10 t +2 \\
x \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.148 |
|
| 22329 |
\begin{align*}
{y^{\prime }}^{r}-a y^{s}-b \,x^{\frac {r s}{r -s}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.157 |
|
| 22330 |
\begin{align*}
x y^{2}+x -2 y+3+\left (x^{2} y-2 y-2 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.160 |
|
| 22331 |
\begin{align*}
y^{\prime } \left (1+\sinh \left (x \right )\right ) \sinh \left (y\right )+\cosh \left (x \right ) \left (\cosh \left (y\right )-1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.170 |
|
| 22332 |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.178 |
|
| 22333 |
\begin{align*}
x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {5 \pi }{4} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
9.183 |
|
| 22334 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y+g \left (x \right ) y^{k} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.188 |
|
| 22335 |
\begin{align*}
y^{\prime } x -x \left (-x +y\right ) \sqrt {x^{2}+y^{2}}-y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.191 |
|
| 22336 |
\begin{align*}
y y^{\prime } x +1+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.192 |
|
| 22337 |
\begin{align*}
y^{\prime }&=-\left (n +1\right ) x^{n} y^{2}+x^{n +1} f \left (x \right ) y-f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
9.196 |
|
| 22338 |
\begin{align*}
y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.197 |
|
| 22339 |
\begin{align*}
\left (1-2 x \right ) y^{\prime }&=16+32 x -6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.201 |
|
| 22340 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.204 |
|
| 22341 |
\begin{align*}
y^{\prime } x +y&=x^{3} y^{6} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.209 |
|
| 22342 |
\begin{align*}
y^{\prime } x&=y \left (1-2 y\right ) \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.210 |
|
| 22343 |
\begin{align*}
y^{\prime \prime }&=a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.211 |
|
| 22344 |
\begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=2 \left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right ) \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
9.214 |
|
| 22345 |
\begin{align*}
\left (x +2 y\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.230 |
|
| 22346 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+3 y^{2}}{2 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.232 |
|
| 22347 |
\begin{align*}
y^{\prime }&=y \left (y^{2}+y \,{\mathrm e}^{b x}+{\mathrm e}^{2 b x}\right ) {\mathrm e}^{-2 b x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.233 |
|
| 22348 |
\begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.233 |
|
| 22349 |
\begin{align*}
y^{\prime }&=y^{3} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.237 |
|
| 22350 |
\begin{align*}
2 y y^{\prime } x^{3}+3 y^{2} x^{2}+7&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.241 |
|
| 22351 |
\begin{align*}
y^{\prime }&=\left (y-2\right ) \left (y+1-\cos \left (t \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.245 |
|
| 22352 |
\begin{align*}
y^{\prime }&=\frac {a^{3} x^{3} y^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1+a^{2} x}{x^{3} a^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.251 |
|
| 22353 |
\begin{align*}
y^{\prime } x +y&=a \left (x^{2}+1\right ) y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.254 |
|
| 22354 |
\begin{align*}
x {y^{\prime }}^{2}+x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.254 |
|
| 22355 |
\begin{align*}
-y+x \left (x +3\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
9.263 |
|
| 22356 |
\begin{align*}
\left (x^{2}+a y^{2}\right ) y^{\prime }&=y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.265 |
|
| 22357 |
\begin{align*}
x \csc \left (\frac {y}{x}\right )-y+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.270 |
|
| 22358 |
\begin{align*}
y^{\prime }+x y^{3}+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.271 |
|
| 22359 |
\begin{align*}
{y^{\prime }}^{2} \sqrt {y}&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.274 |
|
| 22360 |
\begin{align*}
\left (x -y\right ) y^{\prime }&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.279 |
|
| 22361 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +3 y&=5 x^{2} \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.279 |
|
| 22362 |
\begin{align*}
y^{\prime \prime } \left (1+2 \ln \left (y^{\prime }\right )\right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.279 |
|
| 22363 |
\begin{align*}
y^{\prime }&=\frac {1}{\left (y+t \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.280 |
|
| 22364 |
\begin{align*}
y^{\prime }&=\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x \right ) y}{x \left (x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.283 |
|
| 22365 |
\begin{align*}
y^{\prime }&=\frac {x +2 y}{x +2 y+3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.290 |
|
| 22366 |
\begin{align*}
3 y^{\prime } y^{2} x +3 y^{3}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.292 |
|
| 22367 |
\begin{align*}
x^{\prime \prime }&=x-x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.292 |
|
| 22368 |
\begin{align*}
2 y y^{\prime } x -2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.301 |
|
| 22369 |
\begin{align*}
y^{\prime }&=\frac {y^{{3}/{2}}}{y^{{3}/{2}}+x^{2}-2 y x +y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.302 |
|
| 22370 |
\begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.306 |
|
| 22371 |
\begin{align*}
y^{\prime \prime } x +\left (x +a +b \right ) y^{\prime }+a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.309 |
|
| 22372 |
\begin{align*}
x^{2} \left (-y+y^{\prime } x \right )&=y \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.315 |
|
| 22373 |
\begin{align*}
x^{2} y^{\prime }-3 y x -2 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.320 |
|
| 22374 |
\begin{align*}
y^{\prime }&=\frac {\left (x^{4}+3 x y^{2}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.321 |
|
| 22375 |
\begin{align*}
\left (2 x -2 y+5\right ) y^{\prime }&=x -y+3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.333 |
|
| 22376 |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}-y x -x^{2}-\frac {1}{x}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.336 |
|
| 22377 |
\begin{align*}
y^{\prime }&=\frac {t}{y-2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.339 |
|
| 22378 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \left ({\mathrm e}^{x}-{\mathrm e}^{y}\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
9.343 |
|
| 22379 |
\begin{align*}
y^{\prime }&=\frac {-32 y x +16 x^{3}+16 x^{2}-32 x -64 y^{3}+48 y^{2} x^{2}+96 x y^{2}-12 x^{4} y-48 x^{3} y-48 x^{2} y+x^{6}+6 x^{5}+12 x^{4}}{-64 y+16 x^{2}+32 x -64} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.344 |
|
| 22380 |
\begin{align*}
y^{\prime }&=\frac {2+3 x y^{2}}{4 x^{2} y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.346 |
|
| 22381 |
\begin{align*}
x \cos \left (\frac {y}{x}\right )^{2}-y+y^{\prime } x&=0 \\
y \left (1\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.346 |
|
| 22382 |
\begin{align*}
y^{\prime }&=\sin \left (\frac {y}{x}\right )-\cos \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.347 |
|
| 22383 |
\begin{align*}
y^{2} {y^{\prime \prime }}^{2}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.351 |
|
| 22384 |
\begin{align*}
y^{\prime }&=\frac {-3 x^{2}-2 y^{2}}{4 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.354 |
|
| 22385 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=2 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.356 |
|
| 22386 |
\begin{align*}
\left (5 x -2 y+7\right ) y^{\prime }&=10 x -4 y+6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.359 |
|
| 22387 |
\begin{align*}
\left (a +b \sinh \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.366 |
|
| 22388 |
\begin{align*}
a^{2} \left (y^{\prime }-1\right )&=x^{2} y^{\prime }+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.368 |
|
| 22389 |
\begin{align*}
{y^{\prime }}^{2}-4 y^{3}+a y+b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.369 |
|
| 22390 |
\begin{align*}
\left (x^{2}+4 y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.372 |
|
| 22391 |
\begin{align*}
y^{\prime }+\frac {6 y}{x}&=\frac {3 y^{{2}/{3}} \cos \left (x \right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.374 |
|
| 22392 |
\begin{align*}
y^{\prime }&=1+y+y^{2} \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
9.375 |
|
| 22393 |
\begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.376 |
|
| 22394 |
\begin{align*}
y^{\prime }&=\frac {2 a x}{-x^{3} y+2 a \,x^{3}+2 a y^{4} x^{3}-16 y^{2} a^{2} x^{2}+32 a^{3} x +2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
9.376 |
|
| 22395 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=-1+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.386 |
|
| 22396 |
\begin{align*}
x^{2} {y^{\prime }}^{2}+2 x \left (2 x +y\right ) y^{\prime }-4 a +y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.388 |
|
| 22397 |
\begin{align*}
y^{\prime }&=\frac {\left (-256 a \,x^{2} y-32 a^{2} x^{6}-256 a \,x^{2}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512 y+64 x^{4} a +512} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.389 |
|
| 22398 |
\begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+a y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
9.392 |
|
| 22399 |
\begin{align*}
\frac {1+8 x y^{{2}/{3}}}{x^{{2}/{3}} y^{{1}/{3}}}+\frac {\left (2 x^{{4}/{3}} y^{{2}/{3}}-x^{{1}/{3}}\right ) y^{\prime }}{y^{{4}/{3}}}&=0 \\
y \left (1\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
9.397 |
|
| 22400 |
\begin{align*}
y^{\prime \prime } x +\left (x +b \right ) y^{\prime }+a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.398 |
|