| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 19301 |
\begin{align*}
4 y t +\left (t^{2}+1\right ) y^{\prime }&=\frac {1}{\left (t^{2}+1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.812 |
|
| 19302 |
\begin{align*}
\left (3+6 y x +x^{2}\right ) y^{\prime }+2 x +2 y x +3 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.812 |
|
| 19303 |
\begin{align*}
4 y^{\prime \prime }-y&=0 \\
y \left (-2\right ) &= 1 \\
y^{\prime }\left (-2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.812 |
|
| 19304 |
\begin{align*}
3 y y^{\prime }+y^{\prime \prime }&=f \left (x \right )+g \left (x \right ) y-y^{3} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3.815 |
|
| 19305 |
\begin{align*}
y y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.816 |
|
| 19306 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.816 |
|
| 19307 |
\begin{align*}
x y^{\prime }+y&=3 y x \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.817 |
|
| 19308 |
\begin{align*}
y^{\prime }&=2 y^{2}+x y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.817 |
|
| 19309 |
\begin{align*}
\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.817 |
|
| 19310 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=\operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.818 |
|
| 19311 |
\begin{align*}
x^{\prime }&=2 x+y-z+5 \sin \left (t \right ) \\
y^{\prime }&=y+z-10 \cos \left (t \right ) \\
z^{\prime }&=x+z+2 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.818 |
|
| 19312 |
\begin{align*}
\frac {y^{\prime }}{x^{2}+1}&=\frac {x}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.820 |
|
| 19313 |
\begin{align*}
y^{3} {y^{\prime }}^{3}-\left (-3 x +1\right ) y^{2} {y^{\prime }}^{2}+3 x^{2} y y^{\prime }+x^{3}-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
3.821 |
|
| 19314 |
\begin{align*}
\left (t +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.821 |
|
| 19315 |
\begin{align*}
y^{\prime }&=\frac {1}{y t +t +y+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.822 |
|
| 19316 |
\begin{align*}
{y^{\prime }}^{n}-f \left (x \right ) g \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.823 |
|
| 19317 |
\begin{align*}
x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.823 |
|
| 19318 |
\begin{align*}
y^{\prime }&=\frac {\left (2 \ln \left (x \right )+1\right ) x}{\sin \left (y\right )+y \cos \left (y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.824 |
|
| 19319 |
\begin{align*}
\cot \left (x \right ) y^{\prime }+y&=2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.824 |
|
| 19320 |
\begin{align*}
x y^{\prime }+3 y&=\frac {3}{x^{{3}/{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.826 |
|
| 19321 |
\begin{align*}
\left (x -1-y^{2}\right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.826 |
|
| 19322 |
\begin{align*}
-y+x y^{\prime }+x^{5} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.826 |
|
| 19323 |
\begin{align*}
y x +3 x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.827 |
|
| 19324 |
\begin{align*}
x y^{\prime }+3 y&=\frac {3}{x^{{3}/{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.828 |
|
| 19325 |
\begin{align*}
x y^{\prime }+y&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.828 |
|
| 19326 |
\begin{align*}
x^{2} y^{\prime }+\left (1-2 x \right ) y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.829 |
|
| 19327 |
\begin{align*}
\left (1-t \right ) y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.830 |
|
| 19328 |
\begin{align*}
3 y+y^{\prime }&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
3.830 |
|
| 19329 |
\begin{align*}
\frac {y}{4}+y^{\prime }&=3+2 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.831 |
|
| 19330 |
\begin{align*}
y^{\prime }&=\frac {1+y}{t +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.832 |
|
| 19331 |
\begin{align*}
\left (x^{2}+y^{2}+x \right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.833 |
|
| 19332 |
\begin{align*}
-x y^{\prime }+y&=y^{\prime } y^{2} {\mathrm e}^{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.834 |
|
| 19333 |
\begin{align*}
y \left (y-2 x y^{\prime }\right )^{3}&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.836 |
|
| 19334 |
\begin{align*}
y^{\prime }&=\frac {y+x^{2}+y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.836 |
|
| 19335 |
\begin{align*}
n \cos \left (n x +m y\right )-m \sin \left (m x +n y\right )+\left (m \cos \left (n x +m y\right )-n \sin \left (m x +n y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.836 |
|
| 19336 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (\cos \left (x \right )^{2} a +b \sin \left (x \right )^{2}+c \right ) y}{\sin \left (x \right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.838 |
|
| 19337 |
\begin{align*}
\left (x^{3}+y^{3}\right ) y^{\prime }+x^{2} \left (a x +3 y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.839 |
|
| 19338 |
\begin{align*}
5 y x -4 y^{2}-6 x^{2}+\left (y^{2}-8 y x +\frac {5 x^{2}}{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.839 |
|
| 19339 |
\begin{align*}
p^{\prime }&=15-20 p \\
p \left (0\right ) &= {\frac {7}{10}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.839 |
|
| 19340 |
\begin{align*}
2 y^{\prime }+x \left (y^{2}-1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.840 |
|
| 19341 |
\begin{align*}
\left (t -2\right ) y^{\prime }+\left (t^{2}-4\right ) y&=\frac {1}{t +2} \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.842 |
|
| 19342 |
\begin{align*}
y^{\prime }&=\frac {x^{3}+2 y}{x^{3}+x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.843 |
|
| 19343 |
\begin{align*}
y \left (x^{3} {\mathrm e}^{y x}-y\right )+x \left (y+x^{3} {\mathrm e}^{y x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.843 |
|
| 19344 |
\begin{align*}
{\mathrm e}^{3 y} \sin \left (x \right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.844 |
|
| 19345 |
\begin{align*}
2 y^{\prime }&=3 \left (-2+y\right )^{{1}/{3}} \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.845 |
|
| 19346 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.845 |
|
| 19347 |
\begin{align*}
\ln \left (y^{\prime }\right )+a \left (x y^{\prime }-y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.845 |
|
| 19348 |
\begin{align*}
\left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime }&=3 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.846 |
|
| 19349 |
\begin{align*}
9 x^{2} y^{\prime \prime }+\left (x^{2}-15 x \right ) y^{\prime }+7 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.846 |
|
| 19350 |
\begin{align*}
y^{\prime }+y x&=y^{5} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.847 |
|
| 19351 |
\begin{align*}
y^{\prime }&=2 \left (x +1\right ) \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.848 |
|
| 19352 |
\begin{align*}
A y+\left (c \,x^{2}+b x +a \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.848 |
|
| 19353 |
\begin{align*}
z^{\prime }&=2 t \left (z-t^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.848 |
|
| 19354 |
\begin{align*}
v^{\prime }&=g -\frac {k v^{2}}{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.849 |
|
| 19355 |
\begin{align*}
3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.851 |
|
| 19356 |
\begin{align*}
y y^{\prime \prime }&=y^{3}-f^{\prime }\left (x \right ) y+f \left (x \right ) y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
3.852 |
|
| 19357 |
\begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\
y \left (1\right ) &= a \\
y^{\prime }\left (1\right ) &= b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.853 |
|
| 19358 |
\begin{align*}
t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=4 t^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.854 |
|
| 19359 |
\begin{align*}
{y^{\prime }}^{2}-4 x y^{\prime }+2 y+2 x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
3.856 |
|
| 19360 |
\begin{align*}
x y^{\prime }&=x^{n} \ln \left (x \right )-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.857 |
|
| 19361 |
\begin{align*}
2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.858 |
|
| 19362 |
\begin{align*}
a -2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.858 |
|
| 19363 |
\begin{align*}
x y y^{\prime }&=\left (y+1\right ) \left (1-x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.858 |
|
| 19364 |
\begin{align*}
y y^{\prime }-x&=2 y^{2} \\
y \left (1\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.858 |
|
| 19365 |
\begin{align*}
y^{\prime }-5 y&=\left (x -1\right ) \sin \left (x \right )+\left (x +1\right ) \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.858 |
|
| 19366 |
\begin{align*}
\left (x \cos \left (y\right )+\sin \left (2 y\right )\right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.858 |
|
| 19367 |
\begin{align*}
x y^{\prime }+3 y-10 x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.859 |
|
| 19368 |
\begin{align*}
\left (y^{3}+1\right ) y^{\prime }&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.859 |
|
| 19369 |
\begin{align*}
y-\frac {x y^{\prime }}{2}-\frac {x}{2 y^{\prime }}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.861 |
|
| 19370 |
\begin{align*}
\left (1-x \right ) y^{\prime }-y-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.862 |
|
| 19371 |
\begin{align*}
\left (x^{2}+y^{2}-2 y\right ) y^{\prime }&=2 x \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✗ |
✓ |
✓ |
3.863 |
|
| 19372 |
\begin{align*}
2 x -3 y+4+3 \left (x -1\right ) y^{\prime }&=0 \\
y \left (-1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.863 |
|
| 19373 |
\begin{align*}
2 x y \cos \left (x^{2}\right )-2 y x +1+\left (\sin \left (x^{2}\right )-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.864 |
|
| 19374 |
\begin{align*}
6 x^{3} y^{\prime }&=4 x^{2} y+\left (-3 x +1\right ) y^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.865 |
|
| 19375 |
\begin{align*}
2 y+t y^{\prime }&=\frac {\sin \left (t \right )}{t} \\
y \left (-\frac {\pi }{2}\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.865 |
|
| 19376 |
\begin{align*}
a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+y^{2}-a \left (a -1\right ) x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
3.866 |
|
| 19377 |
\begin{align*}
4 y+x y^{\prime }&=x^{3}-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.867 |
|
| 19378 |
\begin{align*}
y^{\prime \prime }+k^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.869 |
|
| 19379 |
\begin{align*}
2 x \left (x^{2}-1\right ) y^{\prime }+2 \left (x^{2}-1\right ) y^{2}-\left (3 x^{2}-5\right ) y+x^{2}-3&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.869 |
|
| 19380 |
\begin{align*}
r^{\prime \prime }-a^{2} r&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.869 |
|
| 19381 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.869 |
|
| 19382 |
\begin{align*}
x^{2} y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.871 |
|
| 19383 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }-n y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.873 |
|
| 19384 |
\begin{align*}
y^{\prime }-\frac {3 y}{t}&=2 t^{3} {\mathrm e}^{2 t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.873 |
|
| 19385 |
\begin{align*}
y-2 y x -x^{2}+x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.874 |
|
| 19386 |
\begin{align*}
x^{2} y^{\prime }&=a -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| 19387 |
\begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=a \,x^{3}+\left (-2 x^{2}+1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| 19388 |
\begin{align*}
-2 a^{2} x y^{\prime }+\left (-a^{2} x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| 19389 |
\begin{align*}
x^{\prime \prime }+256 x&=0 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| 19390 |
\begin{align*}
x^{\prime }+2 x t +t x^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| 19391 |
\begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| 19392 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=\left (1-x y^{3}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.876 |
|
| 19393 |
\begin{align*}
y^{\prime \prime }+2 x^{2} y^{\prime }+4 y x&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.876 |
|
| 19394 |
\begin{align*}
2 y t +y^{\prime }&=2 t \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.877 |
|
| 19395 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.879 |
|
| 19396 |
\begin{align*}
x^{n -1} {y^{\prime }}^{n}-n x y^{\prime }+y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.881 |
|
| 19397 |
\begin{align*}
y^{\prime }&=-\frac {i \left (8 i x +16 y^{4}+8 x^{2} y^{2}+x^{4}\right )}{32 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.881 |
|
| 19398 |
\begin{align*}
y^{\prime }-y \cot \left (x \right )&=y^{2} \sec \left (x \right )^{2} \\
y \left (\frac {\pi }{4}\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.882 |
|
| 19399 |
\begin{align*}
i^{\prime }+2 i&=10 \,{\mathrm e}^{-2 t} \\
i \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.882 |
|
| 19400 |
\begin{align*}
y^{\prime }&=\sin \left (y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.882 |
|