| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 16301 |
\begin{align*}
x^{\prime }+2 x&=6 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.958 |
|
| 16302 |
\begin{align*}
\left (x +1\right ) \left (x -2\right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.959 |
|
| 16303 |
\begin{align*}
2 y-\left (2+x \right ) y^{\prime }+\left (2+x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.959 |
|
| 16304 |
\begin{align*}
y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{2 x \left (x^{2}+1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.959 |
|
| 16305 |
\begin{align*}
y^{\prime \prime }+\lambda ^{2} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.964 |
|
| 16306 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2} \\
x_{2}^{\prime }&=-4 x_{1}+3 x_{2}+10 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.964 |
|
| 16307 |
\begin{align*}
\sqrt {t}\, \sin \left (t \right ) y+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.965 |
|
| 16308 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=1 \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.967 |
|
| 16309 |
\begin{align*}
\left (x -4\right ) y^{\prime \prime }+4 y^{\prime }-\frac {4 y}{x -4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.967 |
|
| 16310 |
\begin{align*}
y^{\prime } x&=y+x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.968 |
|
| 16311 |
\begin{align*}
y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.969 |
|
| 16312 |
\begin{align*}
y-\left (x -2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.970 |
|
| 16313 |
\begin{align*}
y^{\prime }&=\left (a \,{\mathrm e}^{x}+y\right ) y^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.970 |
|
| 16314 |
\begin{align*}
3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z&=0 \\
z \left (1\right ) &= 2 \\
z^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.970 |
|
| 16315 |
\begin{align*}
y^{\prime } x&=3 y+x^{4} \cos \left (x \right ) \\
y \left (2 \pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.971 |
|
| 16316 |
\begin{align*}
\left (x^{2}-y\right ) y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.971 |
|
| 16317 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.971 |
|
| 16318 |
\begin{align*}
\left (b x +a \right ) y+y^{\prime }+2 y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.972 |
|
| 16319 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (3 x \right )+4 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.972 |
|
| 16320 |
\begin{align*}
y^{\prime }&=y^{2}-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.973 |
|
| 16321 |
\begin{align*}
4 x^{2} y^{\prime \prime }-\left (-4 k x +4 m^{2}+x^{2}-1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.973 |
|
| 16322 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&=20 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.973 |
|
| 16323 |
\begin{align*}
y^{\prime }&=-y^{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.973 |
|
| 16324 |
\begin{align*}
a y y^{\prime }+2 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.974 |
|
| 16325 |
\begin{align*}
y y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.974 |
|
| 16326 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.976 |
|
| 16327 |
\begin{align*}
a^{2} y+y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.977 |
|
| 16328 |
\begin{align*}
50 x \left (-1+x \right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.977 |
|
| 16329 |
\begin{align*}
y^{\prime }-a y^{n}-b \,x^{\frac {n}{1-n}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.978 |
|
| 16330 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=8 \delta \left (t \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.979 |
|
| 16331 |
\begin{align*}
y^{\prime }&=\frac {x \left (1+x^{2}+y^{2}\right )}{-y^{3}-x^{2} y-y+y^{6}+3 x^{2} y^{4}+3 y^{2} x^{4}+x^{6}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.980 |
|
| 16332 |
\begin{align*}
m y^{\prime \prime }+a y^{\prime }+k y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.980 |
|
| 16333 |
\begin{align*}
\operatorname {a2} y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.981 |
|
| 16334 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x +1 \\
y \left (0\right ) &= 1 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.981 |
|
| 16335 |
\begin{align*}
y^{\prime \prime }+l y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.983 |
|
| 16336 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.984 |
|
| 16337 |
\begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.984 |
|
| 16338 |
\begin{align*}
2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.984 |
|
| 16339 |
\begin{align*}
y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.985 |
|
| 16340 |
\begin{align*}
y y^{\prime \prime }&=-{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.985 |
|
| 16341 |
\begin{align*}
\frac {y}{t}+\ln \left (y\right )+\left (\frac {t}{y}+\ln \left (t \right )\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.986 |
|
| 16342 |
\begin{align*}
2 y^{\prime \prime }-7 y^{\prime }+3&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.987 |
|
| 16343 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.987 |
|
| 16344 |
\begin{align*}
y^{\prime } x +\left (\sin \left (y\right )-3 \cos \left (y\right ) x^{2}\right ) \cos \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.990 |
|
| 16345 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-\nu ^{2}+x^{2}\right ) y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.990 |
|
| 16346 |
\begin{align*}
x \left (-1+x \right ) y^{\prime }&=\cot \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.991 |
|
| 16347 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{t} \cos \left (2 t \right )+{\mathrm e}^{2 t} \left (3 t +4\right ) \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.992 |
|
| 16348 |
\begin{align*}
y^{\prime }+y&=y^{4} {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.993 |
|
| 16349 |
\begin{align*}
y^{\prime }&=y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.994 |
|
| 16350 |
\begin{align*}
x^{5} y^{\prime }&=1-3 x^{4} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.994 |
|
| 16351 |
\begin{align*}
\left (x +1\right ) \left (3 x -1\right ) y^{\prime \prime }+\cos \left (x \right ) y^{\prime }-3 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.994 |
|
| 16352 |
\begin{align*}
y^{\prime }&=\sin \left (x -y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.997 |
|
| 16353 |
\begin{align*}
y^{\prime \prime \prime }-a^{2} \left ({y^{\prime }}^{5}+2 {y^{\prime }}^{3}+y^{\prime }\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.997 |
|
| 16354 |
\begin{align*}
t^{2}-y+\left (y-t \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.997 |
|
| 16355 |
\begin{align*}
\sin \left (x \right ) y^{\prime }+2 \cos \left (x \right ) y&=1 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.999 |
|
| 16356 |
\begin{align*}
{y^{\prime }}^{2}+a y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.999 |
|
| 16357 |
\begin{align*}
y^{\prime }&=y+y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.000 |
|
| 16358 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
4.000 |
|
| 16359 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.000 |
|
| 16360 |
\begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.001 |
|
| 16361 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.001 |
|
| 16362 |
\begin{align*}
t +y+1-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.002 |
|
| 16363 |
\begin{align*}
x^{\prime }+x \tanh \left (t \right )&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.003 |
|
| 16364 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=3 \delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.003 |
|
| 16365 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=\csc \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.003 |
|
| 16366 |
\begin{align*}
y^{\prime } \sqrt {a^{2}+x^{2}}+x +y&=\sqrt {a^{2}+x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.004 |
|
| 16367 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.006 |
|
| 16368 |
\begin{align*}
y^{\prime }&=\sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.006 |
|
| 16369 |
\begin{align*}
x^{4} {y^{\prime }}^{2}+2 y y^{\prime } x^{3}-4&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.006 |
|
| 16370 |
\begin{align*}
y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.006 |
|
| 16371 |
\begin{align*}
y \left (1+y\right ) y^{\prime }&=x \left (x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.007 |
|
| 16372 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-3 y y^{\prime } x +x^{3}+2 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.007 |
|
| 16373 |
\begin{align*}
-y+y^{\prime } x&=2 x^{2}-3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.007 |
|
| 16374 |
\begin{align*}
y \ln \left (t \right )+\left (t -3\right ) y^{\prime }&=2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.008 |
|
| 16375 |
\begin{align*}
-y+y^{\prime } t&=t^{3} {\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.009 |
|
| 16376 |
\begin{align*}
y^{\prime } x&=-a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.010 |
|
| 16377 |
\begin{align*}
2 y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.010 |
|
| 16378 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x} \left (a +b \,{\mathrm e}^{-y}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.012 |
|
| 16379 |
\begin{align*}
y^{\prime }+a y&=b \sin \left (k x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.012 |
|
| 16380 |
\begin{align*}
s^{2} t^{\prime \prime }+s t t^{\prime }&=s \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.012 |
|
| 16381 |
\begin{align*}
\left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+b^{2}+x^{2}+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.013 |
|
| 16382 |
\begin{align*}
y^{\prime }-y x&=\frac {x}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.014 |
|
| 16383 |
\begin{align*}
2 y+y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.016 |
|
| 16384 |
\begin{align*}
y+y^{\prime }&=\frac {{\mathrm e}^{t}}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.016 |
|
| 16385 |
\begin{align*}
t y^{\prime \prime }+t^{2} y^{\prime }-\sin \left (t \right ) \sqrt {t}&=t^{2}-t +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.016 |
|
| 16386 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=\left (1-x y^{3}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.017 |
|
| 16387 |
\begin{align*}
y-2 x^{3} \tan \left (\frac {y}{x}\right )-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.019 |
|
| 16388 |
\begin{align*}
y^{\prime }&=\frac {2 y}{\pi }-\sin \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.019 |
|
| 16389 |
\begin{align*}
y^{\prime }&=\frac {1-2 x}{y} \\
y \left (1\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.020 |
|
| 16390 |
\begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=\left (x^{2}-x +1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.020 |
|
| 16391 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.020 |
|
| 16392 |
\begin{align*}
y^{\prime }&=\frac {\left (x^{2}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.020 |
|
| 16393 |
\begin{align*}
y^{\prime }&=\frac {3 x}{y+x^{2} y} \\
y \left (0\right ) &= -7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.020 |
|
| 16394 |
\begin{align*}
y^{\prime }&=\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.022 |
|
| 16395 |
\begin{align*}
x {y^{\prime }}^{2}+y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.024 |
|
| 16396 |
\begin{align*}
y^{\prime }&=\frac {2 x \left (-1+y\right )}{x^{2}+3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.026 |
|
| 16397 |
\begin{align*}
y y^{\prime }&=-1+x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.027 |
|
| 16398 |
\begin{align*}
x {y^{\prime }}^{2}&=\left (a -x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.027 |
|
| 16399 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.028 |
|
| 16400 |
\begin{align*}
y^{\prime } x +y&=x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.028 |
|