| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15301 |
\begin{align*}
x^{\prime }&=-2 x+3 \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.862 |
|
| 15302 |
\begin{align*}
y^{\prime }&=3 x +y \\
y \left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.862 |
|
| 15303 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.863 |
|
| 15304 |
\begin{align*}
3 y+x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.863 |
|
| 15305 |
\begin{align*}
\sin \left (y^{\prime }\right )&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.864 |
|
| 15306 |
\begin{align*}
y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.865 |
|
| 15307 |
\begin{align*}
y^{\prime }-2 y t&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.865 |
|
| 15308 |
\begin{align*}
{y^{\prime }}^{2}+x y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.865 |
|
| 15309 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{3}+b x \right ) y^{\prime }+2 \left (2 a \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.865 |
|
| 15310 |
\begin{align*}
x^{\prime }&=a x+b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.865 |
|
| 15311 |
\begin{align*}
4 y^{\prime \prime }+8 y^{\prime }&=x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.865 |
|
| 15312 |
\begin{align*}
2 x^{\prime }-x+7 y^{\prime }+3 y&=90 \sin \left (2 t \right ) \\
x^{\prime }-5 x+8 y^{\prime }-3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.865 |
|
| 15313 |
\begin{align*}
\left (x -y\right ) y^{\prime \prime }&=\left (y^{\prime }+1\right ) \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.866 |
|
| 15314 |
\begin{align*}
x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.866 |
|
| 15315 |
\begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.867 |
|
| 15316 |
\begin{align*}
y+\left (1-x \right ) y^{\prime }+2 x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.868 |
|
| 15317 |
\begin{align*}
\left (1+3 x \right ) y-4 x^{2} y^{\prime }+4 x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.868 |
|
| 15318 |
\begin{align*}
\left (x +3\right )^{2} y^{\prime \prime }+3 \left (x +3\right ) y^{\prime }+5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.868 |
|
| 15319 |
\begin{align*}
{y^{\prime }}^{3}-2 x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.868 |
|
| 15320 |
\begin{align*}
x^{2}+y-x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.868 |
|
| 15321 |
\begin{align*}
y^{\prime }&=\left (-1+y\right )^{2}-\frac {1}{100} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
1.869 |
|
| 15322 |
\begin{align*}
\left (x +1\right ) y^{\prime }+y \left (-x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.869 |
|
| 15323 |
\begin{align*}
x y y^{\prime \prime }+{y^{\prime }}^{2} x -y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.869 |
|
| 15324 |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{\cos \left (2 x \right )^{{3}/{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.869 |
|
| 15325 |
\begin{align*}
y^{\prime \prime }&=1-\cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.869 |
|
| 15326 |
\begin{align*}
-\frac {u^{\prime \prime }}{2}&=x \\
u \left (0\right ) &= 0 \\
u \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.869 |
|
| 15327 |
\begin{align*}
2 x y^{\prime }-y&=\sin \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.869 |
|
| 15328 |
\begin{align*}
b y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.870 |
|
| 15329 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.870 |
|
| 15330 |
\begin{align*}
y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.870 |
|
| 15331 |
\begin{align*}
y^{\prime }&=y-x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.870 |
|
| 15332 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.871 |
|
| 15333 |
\begin{align*}
x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.871 |
|
| 15334 |
\begin{align*}
3 y^{\prime }&=4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.871 |
|
| 15335 |
\begin{align*}
-2 y-2 \left (2 x +1\right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.872 |
|
| 15336 |
\begin{align*}
3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.872 |
|
| 15337 |
\begin{align*}
y^{\prime }&=x +y \\
y \left (-2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.872 |
|
| 15338 |
\begin{align*}
x^{6} y^{\prime \prime }+x^{3} \left (3 x^{2}+a \right ) y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.872 |
|
| 15339 |
\begin{align*}
y^{\prime }&=1+y x +3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.872 |
|
| 15340 |
\begin{align*}
y^{\prime \prime }+4 y&=2 \delta \left (t -\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.872 |
|
| 15341 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.873 |
|
| 15342 |
\begin{align*}
a y y^{\prime }+2 {y^{\prime }}^{2} x +x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.873 |
|
| 15343 |
\begin{align*}
x_{1}^{\prime }&=-5 x_{1}+x_{2}-4 x_{3}-x_{4} \\
x_{2}^{\prime }&=-3 x_{2} \\
x_{3}^{\prime }&=x_{1}-x_{2}+x_{4} \\
x_{4}^{\prime }&=2 x_{1}-x_{2}+2 x_{3}-2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.873 |
|
| 15344 |
\begin{align*}
y^{\prime \prime }-4 y&=31 \\
y \left (0\right ) &= -9 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.874 |
|
| 15345 |
\begin{align*}
4 {y^{\prime }}^{2} x^{2}-4 x y y^{\prime }&=8 x^{3}-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.875 |
|
| 15346 |
\begin{align*}
\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.875 |
|
| 15347 |
\begin{align*}
y^{\prime }-\left (A y-a \right ) \left (B y-b \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.875 |
|
| 15348 |
\begin{align*}
x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.875 |
|
| 15349 |
\begin{align*}
y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.875 |
|
| 15350 |
\begin{align*}
y^{\prime }&=y^{3}+{\mathrm e}^{-5 t} \\
y \left (0\right ) &= {\frac {2}{5}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.876 |
|
| 15351 |
\begin{align*}
-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.876 |
|
| 15352 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
y \left (1\right ) &= 5 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.876 |
|
| 15353 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.877 |
|
| 15354 |
\begin{align*}
x&=\left (x^{2}-2 y+1\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.877 |
|
| 15355 |
\begin{align*}
x y^{\prime \prime }+3 y^{\prime }+x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.878 |
|
| 15356 |
\begin{align*}
y^{\prime }+4 y&=y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.878 |
|
| 15357 |
\begin{align*}
x^{\prime }&=\lambda x-x^{3}-x^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.878 |
|
| 15358 |
\begin{align*}
\left (-x +3\right ) y-\left (-3 x +4\right ) y^{\prime }+\left (1-2 x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.879 |
|
| 15359 |
\begin{align*}
y^{\prime }&=\frac {-{\mathrm e}^{-x}+x}{x +{\mathrm e}^{y}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.881 |
|
| 15360 |
\begin{align*}
x^{\prime }&=4 x-13 y \\
y^{\prime }&=x+19 \cos \left (4 t \right )-13 \sin \left (4 t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 13 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.881 |
|
| 15361 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.882 |
|
| 15362 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.883 |
|
| 15363 |
\begin{align*}
y^{\prime }+y&=x y^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.884 |
|
| 15364 |
\begin{align*}
2 y+y^{\prime }&=\frac {x}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.884 |
|
| 15365 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=\left (x^{2}-1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.884 |
|
| 15366 |
\begin{align*}
x y^{\prime }+y&=2 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.885 |
|
| 15367 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y&=x^{a +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.885 |
|
| 15368 |
\begin{align*}
x^{2} \left (-1+y\right ) y^{\prime \prime }-2 {y^{\prime }}^{2} x^{2}-2 x \left (-1+y\right ) y^{\prime }-2 y \left (-1+y\right )^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
1.885 |
|
| 15369 |
\begin{align*}
a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.886 |
|
| 15370 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x +1}-\frac {\left (x +2\right ) y}{x^{2} \left (x +1\right )}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.886 |
|
| 15371 |
\begin{align*}
y^{\prime }&=x^{2}-2 y x +y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.887 |
|
| 15372 |
\begin{align*}
y&=-x y^{\prime }+x^{4} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.887 |
|
| 15373 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=\left \{\begin {array}{cc} x & 0\le x <1 \\ -x & 1\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.888 |
|
| 15374 |
\begin{align*}
y^{\prime \prime }&=t^{2}+{\mathrm e}^{t}+\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.888 |
|
| 15375 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.890 |
|
| 15376 |
\begin{align*}
y^{3} y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.891 |
|
| 15377 |
\begin{align*}
y^{\prime }&=2 x \sec \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.891 |
|
| 15378 |
\begin{align*}
x y^{\prime \prime }&=y^{\prime }+x^{5} \\
y \left (1\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.891 |
|
| 15379 |
\begin{align*}
y^{\prime }&=\sin \left (x \right )+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.891 |
|
| 15380 |
\begin{align*}
3 y y^{\prime \prime }-5 {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.891 |
|
| 15381 |
\begin{align*}
y^{\prime \prime }+9 y&=24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.891 |
|
| 15382 |
\begin{align*}
\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.892 |
|
| 15383 |
\begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
1.892 |
|
| 15384 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=\cos \left (a x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.893 |
|
| 15385 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y&=3 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.893 |
|
| 15386 |
\begin{align*}
a y^{\prime \prime }+b y^{\prime }+c y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.894 |
|
| 15387 |
\begin{align*}
x y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.894 |
|
| 15388 |
\begin{align*}
x^{\prime \prime }&=3 t \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.895 |
|
| 15389 |
\begin{align*}
y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +a \,x^{2}+\left (1-a \right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.895 |
|
| 15390 |
\begin{align*}
y^{\prime }&=\frac {i x^{2} \left (i-2 \sqrt {-x^{3}+6 y}\right )}{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.895 |
|
| 15391 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.895 |
|
| 15392 |
\begin{align*}
x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y&=8 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.895 |
|
| 15393 |
\begin{align*}
x^{2} y^{\prime }+2 y x&={\mathrm e}^{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.895 |
|
| 15394 |
\begin{align*}
\frac {1+2 x y}{x^{\prime }}&=y^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.896 |
|
| 15395 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.896 |
|
| 15396 |
\begin{align*}
x&={y^{\prime }}^{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.896 |
|
| 15397 |
\begin{align*}
y^{\prime }&=\left (4 x +y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.897 |
|
| 15398 |
\begin{align*}
-\cos \left (x \right ) y-\sin \left (x \right ) y^{\prime }+y^{\prime \prime }&=a -x +x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.897 |
|
| 15399 |
\begin{align*}
\left (2 x +1\right ) y^{\prime }&=4 x +2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.897 |
|
| 15400 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+2 x_{2}-2 x_{4} \\
x_{2}^{\prime }&=-x_{1}+3 x_{2}-x_{3}+x_{4} \\
x_{3}^{\prime }&=-2 x_{1}-2 x_{2}-4 x_{3}+2 x_{4} \\
x_{4}^{\prime }&=-7 x_{1}+x_{2}-7 x_{3}+3 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.898 |
|