| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15401 |
\begin{align*}
2 t y+y^{\prime }&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.526 |
|
| 15402 |
\begin{align*}
x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.527 |
|
| 15403 |
\begin{align*}
y^{\prime }&=f \left (x \right ) g \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.528 |
|
| 15404 |
\begin{align*}
L i^{\prime }+R i&=E_{0} \\
i \left (0\right ) &= i_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.528 |
|
| 15405 |
\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*} |
✓ |
✓ |
✓ |
✗ |
1.529 |
|
| 15406 |
\begin{align*}
y^{\prime \prime }-\left (\frac {1}{x}+2\right ) y^{\prime }+\left (x +\frac {1}{x^{2}}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.529 |
|
| 15407 |
\begin{align*}
y^{\prime \prime }&=\frac {\left (2 x^{2}-1\right ) y^{\prime }}{x^{3}}-\frac {2 y}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.530 |
|
| 15408 |
\begin{align*}
2 x^{2} y^{\prime \prime }+10 y^{\prime } x +8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.530 |
|
| 15409 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.531 |
|
| 15410 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }&=2 \cos \left (4 x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.531 |
|
| 15411 |
\begin{align*}
y^{\prime } x +x^{2}-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.532 |
|
| 15412 |
\begin{align*}
y^{\prime } x +a y^{2}-y+b \,x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.532 |
|
| 15413 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.532 |
|
| 15414 |
\begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.532 |
|
| 15415 |
\begin{align*}
y^{\prime \prime }+9 y&=5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.533 |
|
| 15416 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (\left (\operatorname {a1} +\operatorname {b1} +1\right ) x -\operatorname {d1} \right ) y^{\prime }+\operatorname {a1} \operatorname {b1} \operatorname {d1}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.533 |
|
| 15417 |
\begin{align*}
y^{\prime }&=\frac {y+x^{2}}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.533 |
|
| 15418 |
\begin{align*}
y^{\prime }&=\frac {2 y}{\pi }-\sin \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.533 |
|
| 15419 |
\begin{align*}
y^{\prime }&=y-\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.534 |
|
| 15420 |
\begin{align*}
y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x}&=x -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.534 |
|
| 15421 |
\begin{align*}
y^{\prime }-2 t y&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.535 |
|
| 15422 |
\begin{align*}
y y^{\prime }&=\sqrt {y^{2}+a^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.535 |
|
| 15423 |
\begin{align*}
y^{\prime }&=f \left (x \right ) g \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.535 |
|
| 15424 |
\begin{align*}
y^{\prime }&=1+x +y+y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.536 |
|
| 15425 |
\begin{align*}
x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x&=F \cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.536 |
|
| 15426 |
\begin{align*}
y^{\prime }&=\sec \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.536 |
|
| 15427 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.538 |
|
| 15428 |
\begin{align*}
y^{\prime }&={\mathrm e}^{2 x}+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.539 |
|
| 15429 |
\begin{align*}
y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.539 |
|
| 15430 |
\begin{align*}
x^{\prime }&=2 x+3 y \\
y^{\prime }&=-x-14 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.539 |
|
| 15431 |
\begin{align*}
y^{\prime } x +\left (x +1\right ) y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.539 |
|
| 15432 |
\begin{align*}
y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.540 |
|
| 15433 |
\begin{align*}
y^{\prime }-\cos \left (a y+b x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.540 |
|
| 15434 |
\begin{align*}
y^{\prime \prime }+2 a x y^{\prime }+y a^{2} x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.540 |
|
| 15435 |
\begin{align*}
r^{\prime \prime }+r&=1 \\
r \left (0\right ) &= 0 \\
r^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.540 |
|
| 15436 |
\begin{align*}
y^{\prime \prime }-\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.541 |
|
| 15437 |
\begin{align*}
h^{2}+\frac {2 a h}{\sqrt {1+{h^{\prime }}^{2}}}&=b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.542 |
|
| 15438 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.542 |
|
| 15439 |
\begin{align*}
-\left (-a^{2} x^{2}+p^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| 15440 |
\begin{align*}
\left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.543 |
|
| 15441 |
\begin{align*}
x^{\prime }&=-x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| 15442 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }&=5 t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| 15443 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| 15444 |
\begin{align*}
y y^{\prime \prime }&=y y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.544 |
|
| 15445 |
\begin{align*}
4 y^{\prime \prime }+8 y^{\prime }&=x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.544 |
|
| 15446 |
\begin{align*}
y^{\prime }&=\sqrt {x -y} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.545 |
|
| 15447 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.545 |
|
| 15448 |
\begin{align*}
y+y^{\prime }&=\frac {1}{t^{2}+1} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| 15449 |
\begin{align*}
2 y+y^{\prime }&=b \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| 15450 |
\begin{align*}
x^{\prime \prime }+4 x&=\delta \left (-2+t \right )-\delta \left (t -5\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| 15451 |
\begin{align*}
y^{\prime \prime }&=2 y^{\prime }-6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| 15452 |
\begin{align*}
x_{1}^{\prime }&=-5 x_{1}-2 x_{2}-x_{3}+2 x_{4}+3 x_{5} \\
x_{2}^{\prime }&=-3 x_{2} \\
x_{3}^{\prime }&=x_{1}-x_{3}-x_{5} \\
x_{4}^{\prime }&=2 x_{1}+x_{2}-4 x_{4}-2 x_{5} \\
x_{5}^{\prime }&=-3 x_{1}-2 x_{2}-x_{3}+2 x_{4}+x_{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| 15453 |
\begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| 15454 |
\begin{align*}
y^{\prime \prime }+16 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| 15455 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| 15456 |
\begin{align*}
2 y^{\prime \prime }&={\mathrm e}^{y} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.547 |
|
| 15457 |
\begin{align*}
3 y^{2} y^{\prime }+y^{3}&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.548 |
|
| 15458 |
\begin{align*}
\frac {2 t y}{t^{2}+1}+y^{\prime }&=\frac {1}{t^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.548 |
|
| 15459 |
\begin{align*}
y y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.548 |
|
| 15460 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| 15461 |
\begin{align*}
x^{\prime }&=4 x+3 y+5 \operatorname {Heaviside}\left (-2+t \right ) \\
y^{\prime }&=x+6 y+17 \operatorname {Heaviside}\left (-2+t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| 15462 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (x -1\right )^{2} {\mathrm e}^{x} \\
y \left (-\infty \right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.549 |
|
| 15463 |
\begin{align*}
y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\left (n^{2}+\frac {2}{x^{2}}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| 15464 |
\begin{align*}
2 y+x +\left (x^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| 15465 |
\begin{align*}
x^{\prime }&=3 x-2 y+2 t^{2} \\
y^{\prime }&=5 x+y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| 15466 |
\begin{align*}
2 y^{\prime } x +y&=10 \sqrt {x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| 15467 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| 15468 |
\begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.551 |
|
| 15469 |
\begin{align*}
y^{\prime \prime }&=-\frac {x y^{\prime }}{f \left (x \right )}+\frac {y}{f \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.551 |
|
| 15470 |
\begin{align*}
8 \left (-x^{3}+1\right ) y y^{\prime \prime }-4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}-12 x^{2} y y^{\prime }+3 x y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.551 |
|
| 15471 |
\begin{align*}
7 t^{2} x^{\prime }&=3 x-2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.551 |
|
| 15472 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.551 |
|
| 15473 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=2 \delta \left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.551 |
|
| 15474 |
\begin{align*}
y^{\prime }&=-x^{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.552 |
|
| 15475 |
\begin{align*}
y^{\prime }&=y \left (y+t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.552 |
|
| 15476 |
\begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.552 |
|
| 15477 |
\begin{align*}
3 y^{3}-y x -\left (x^{2}+6 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| 15478 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| 15479 |
\begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=2 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| 15480 |
\begin{align*}
y^{\prime }&=4 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| 15481 |
\begin{align*}
x&=y^{\prime }+{y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| 15482 |
\begin{align*}
-y-\left (-x +2\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.554 |
|
| 15483 |
\begin{align*}
y^{2} {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.554 |
|
| 15484 |
\begin{align*}
y^{\prime }+f \left (x \right ) y-g \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| 15485 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| 15486 |
\begin{align*}
y^{\prime }&=-\frac {1}{2 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| 15487 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2}-2 \,{\mathrm e}^{t} \\
x_{3}^{\prime }&=3 x_{3} \\
x_{4}^{\prime }&=-x_{1}+2 x_{2}+9 x_{3}+x_{4}+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| 15488 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+5 x_{2}+6 x_{3} \\
x_{2}^{\prime }&=8 x_{2}+9 x_{3} \\
x_{3}^{\prime }&=x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.555 |
|
| 15489 |
\begin{align*}
t^{2} y+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.556 |
|
| 15490 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y&=\tan \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.556 |
|
| 15491 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (4 x^{2}+1\right ) y-4 \sqrt {x^{3}}\, {\mathrm e}^{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.556 |
|
| 15492 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2 a +b -1\right ) x y^{\prime }+\left (c^{2} b^{2} x^{2 b}+a \left (a +b \right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.556 |
|
| 15493 |
\begin{align*}
y^{\prime }-7 y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.556 |
|
| 15494 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{2 x}+x^{2}-\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| 15495 |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.557 |
|
| 15496 |
\begin{align*}
y^{\prime }&=\frac {1}{2 x -y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.557 |
|
| 15497 |
\begin{align*}
y^{\prime }&=3 x +2 y \\
y \left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| 15498 |
\begin{align*}
2 y^{3}+2 y^{2}+\left (3 x y^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.558 |
|
| 15499 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.558 |
|
| 15500 |
\begin{align*}
y^{\prime }&=\sin \left (y x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.558 |
|