| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15401 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+2 y^{\prime } x -y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.053 |
|
| 15402 |
\begin{align*}
\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (x +1\right ) y^{\prime }+6 y&=6 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.053 |
|
| 15403 |
\begin{align*}
y^{\prime }&=\frac {2 y-x -4}{2 x -y+5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.056 |
|
| 15404 |
\begin{align*}
y-x +y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.056 |
|
| 15405 |
\begin{align*}
y&=2 y^{\prime } x +\sin \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.056 |
|
| 15406 |
\begin{align*}
y^{\prime }-a y&=f \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.056 |
|
| 15407 |
\begin{align*}
y^{\prime \prime }+\left (a x +2 b \right ) y^{\prime }+\left (a b x +b^{2}-a \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.058 |
|
| 15408 |
\begin{align*}
b y+a y {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.059 |
|
| 15409 |
\begin{align*}
x^{\prime }&=3 x+2 y+3 \\
y^{\prime }&=7 x+5 y+2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| 15410 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} x & 0\le x \le \pi \\ 0 & \pi <x \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| 15411 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {2}{x^{2}}+1 \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.060 |
|
| 15412 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.062 |
|
| 15413 |
\begin{align*}
\left (1+x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.062 |
|
| 15414 |
\begin{align*}
y^{\prime }-2 y x&=-1 \\
y \left (0\right ) &= \frac {\sqrt {\pi }}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.064 |
|
| 15415 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
y \left (2\right ) &= 3 \\
y^{\prime }\left (2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.064 |
|
| 15416 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.064 |
|
| 15417 |
\begin{align*}
4 y^{\prime \prime }-7 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.064 |
|
| 15418 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{x k} y^{2}+b \,{\mathrm e}^{s x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.065 |
|
| 15419 |
\begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.065 |
|
| 15420 |
\begin{align*}
y^{\prime } y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.066 |
|
| 15421 |
\begin{align*}
y^{\prime \prime } x -2 y^{\prime }+\frac {\left (x^{2}+2\right ) y}{x}&=4+\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.066 |
|
| 15422 |
\begin{align*}
x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.067 |
|
| 15423 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.067 |
|
| 15424 |
\begin{align*}
\left ({y^{\prime }}^{2}-y^{2}\right ) {\mathrm e}^{y^{\prime }}-x {y^{\prime }}^{2}+x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.067 |
|
| 15425 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 x \,{\mathrm e}^{2 x}-\sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.068 |
|
| 15426 |
\begin{align*}
\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y+\left (x \cos \left (\frac {y}{x}\right )-y \sin \left (\frac {y}{x}\right )\right ) x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.069 |
|
| 15427 |
\begin{align*}
y y^{\prime \prime }&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.070 |
|
| 15428 |
\begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \ln \left (y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.071 |
|
| 15429 |
\begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.072 |
|
| 15430 |
\begin{align*}
x^{\prime \prime }+\omega ^{2} x&=\sin \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.072 |
|
| 15431 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.073 |
|
| 15432 |
\begin{align*}
y^{\prime }&=\frac {y x +a^{2}}{a^{2}-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.073 |
|
| 15433 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.075 |
|
| 15434 |
\begin{align*}
x^{2} y^{\prime \prime }+a y^{\prime }-\left (b^{2} x^{2}+a b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.075 |
|
| 15435 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.075 |
|
| 15436 |
\begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.075 |
|
| 15437 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\left (y-t \right )^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.076 |
|
| 15438 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 a x +y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.076 |
|
| 15439 |
\begin{align*}
t^{2} y^{\prime \prime }-y^{\prime } t +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.076 |
|
| 15440 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+x&=0 \\
y \left (2\right ) &= -1 \\
y^{\prime }\left (2\right ) &= -{\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.076 |
|
| 15441 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a^{2} x^{2}-n \left (n +1\right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.077 |
|
| 15442 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.077 |
|
| 15443 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.079 |
|
| 15444 |
\begin{align*}
y+y^{\prime }&=t \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.079 |
|
| 15445 |
\begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.079 |
|
| 15446 |
\begin{align*}
x^{2}+y+y^{2}-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.079 |
|
| 15447 |
\begin{align*}
\cos \left (y^{\prime }\right )+y^{\prime } x&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.080 |
|
| 15448 |
\begin{align*}
y^{\prime } x +2 y-\cos \left (x \right ) x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.080 |
|
| 15449 |
\begin{align*}
t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5} \\
y \left (1\right ) &= a \\
y^{\prime }\left (1\right ) &= b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.080 |
|
| 15450 |
\begin{align*}
x^{\prime }+y^{\prime }-x+5 y&=t^{2} \\
x^{\prime }+2 y^{\prime }-2 x+4 y&=2 t +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.081 |
|
| 15451 |
\begin{align*}
a \left (2+a \right )^{2} y y^{\prime \prime }&=-a^{2} f \left (x \right )^{2} y^{4}+a^{2} \left (2+a \right ) y^{3} f^{\prime }\left (x \right )+a \left (2+a \right )^{2} f \left (x \right ) y^{2} y^{\prime }+\left (-1+a \right ) \left (2+a \right )^{2} {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
2.082 |
|
| 15452 |
\begin{align*}
x^{\prime }&=x+t +1 \\
x \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.082 |
|
| 15453 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.082 |
|
| 15454 |
\begin{align*}
x \left (x +1\right )^{2} y y^{\prime \prime }-x \left (x +1\right )^{2} {y^{\prime }}^{2}+2 \left (x +1\right )^{2} y y^{\prime }-a \left (2+x \right ) y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.086 |
|
| 15455 |
\begin{align*}
y^{\prime \prime }-4 y&=\delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.087 |
|
| 15456 |
\begin{align*}
x^{\prime }&=\left (x-1\right ) \left (1-2 x\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.087 |
|
| 15457 |
\begin{align*}
8 {y^{\prime }}^{3} x -12 y {y^{\prime }}^{2}+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.087 |
|
| 15458 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=3+4 \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.087 |
|
| 15459 |
\begin{align*}
y^{\prime \prime }+4 y&=8 \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| 15460 |
\begin{align*}
y^{\prime }+2 y x&=x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| 15461 |
\begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| 15462 |
\begin{align*}
y^{\prime \prime }+\omega ^{2} y&=A \cos \left (\omega x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.089 |
|
| 15463 |
\begin{align*}
4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=\arctan \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.089 |
|
| 15464 |
\begin{align*}
y^{\prime }&=x^{2}+2 x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.089 |
|
| 15465 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime } x +y&=4 x y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.089 |
|
| 15466 |
\begin{align*}
i^{\prime }+3 i&={\mathrm e}^{-2 t} \\
i \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.089 |
|
| 15467 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.090 |
|
| 15468 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{\left (x^{3}+1\right ) y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.091 |
|
| 15469 |
\begin{align*}
{y^{\prime }}^{6}-\left (y-a \right )^{4} \left (y-b \right )^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.091 |
|
| 15470 |
\begin{align*}
y^{\prime }&=2 x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.092 |
|
| 15471 |
\begin{align*}
x_{1}^{\prime }&=x_{2}+x_{3}+1 \\
x_{2}^{\prime }&=x_{3}+x_{4}+t \\
x_{3}^{\prime }&=x_{1}+x_{4}+t^{2} \\
x_{4}^{\prime }&=x_{1}+x_{2}+t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.093 |
|
| 15472 |
\begin{align*}
n^{2} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.093 |
|
| 15473 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.094 |
|
| 15474 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (1+y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.094 |
|
| 15475 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.094 |
|
| 15476 |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2} \left (1-y^{\prime } \cos \left (y\right )+y y^{\prime } \sin \left (y\right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.095 |
|
| 15477 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.095 |
|
| 15478 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.095 |
|
| 15479 |
\begin{align*}
y \left (1+\sqrt {x^{2} y^{4}-1}\right )+2 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.096 |
|
| 15480 |
\begin{align*}
y^{\prime \prime }+16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.097 |
|
| 15481 |
\begin{align*}
x^{\prime }&=\sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.097 |
|
| 15482 |
\begin{align*}
m y^{\prime \prime }+b y^{\prime }+k y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.098 |
|
| 15483 |
\begin{align*}
x^{\prime }+x&={\mathrm e}^{-y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.099 |
|
| 15484 |
\begin{align*}
9 y^{\prime \prime }+49 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.099 |
|
| 15485 |
\begin{align*}
-\left (x +1\right )^{3} y+y^{\prime } x +x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.100 |
|
| 15486 |
\begin{align*}
2 y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.101 |
|
| 15487 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.101 |
|
| 15488 |
\begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.101 |
|
| 15489 |
\begin{align*}
y^{\prime }-2 y x&={\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.102 |
|
| 15490 |
\begin{align*}
y^{\prime }&={\mathrm e}^{2 x -3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.102 |
|
| 15491 |
\begin{align*}
x^{2} y^{2} y^{\prime \prime }-3 y^{\prime } y^{2} x +4 y^{3}+x^{6}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.103 |
|
| 15492 |
\begin{align*}
y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.104 |
|
| 15493 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=8 x^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.104 |
|
| 15494 |
\begin{align*}
y^{\prime }&=\frac {2 \sqrt {-1+y}}{3} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.105 |
|
| 15495 |
\begin{align*}
2 \left (1-y\right ) y y^{\prime \prime }&=\left (1-3 y\right ) {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.105 |
|
| 15496 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }+6 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.105 |
|
| 15497 |
\begin{align*}
y^{\prime }+a y&=\sqrt {1+t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.105 |
|
| 15498 |
\begin{align*}
y x +x^{2} y^{\prime }&=x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.105 |
|
| 15499 |
\begin{align*}
y^{\prime }+3 y&=x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.105 |
|
| 15500 |
\begin{align*}
t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5} \\
y \left (1\right ) &= -1 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.105 |
|