| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 16501 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.365 |
|
| 16502 |
\begin{align*}
{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.365 |
|
| 16503 |
\begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} 1 & 0\le x \le 1 \\ -1 & 1<x \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.366 |
|
| 16504 |
\begin{align*}
x y^{\prime }+y&=x^{2} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.366 |
|
| 16505 |
\begin{align*}
x^{2} y-2 x +\left (\frac {x^{3}}{3}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.366 |
|
| 16506 |
\begin{align*}
{\mathrm e}^{y}&={\mathrm e}^{4 y} y^{\prime }+1 \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
2.366 |
|
| 16507 |
\begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.368 |
|
| 16508 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & \pi \le t <2 \pi \\ 0 & \operatorname {otherwise} \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.368 |
|
| 16509 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.368 |
|
| 16510 |
\begin{align*}
-y^{\prime }+x y^{\prime \prime }&={\mathrm e}^{x} x^{2} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.368 |
|
| 16511 |
\begin{align*}
w^{\prime }&=\frac {w}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.368 |
|
| 16512 |
\begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.368 |
|
| 16513 |
\begin{align*}
a y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.369 |
|
| 16514 |
\begin{align*}
y^{\prime }&=\sqrt {1-x^{2}-y^{2}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.369 |
|
| 16515 |
\begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.369 |
|
| 16516 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.369 |
|
| 16517 |
\begin{align*}
2 y t +y^{\prime }&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.369 |
|
| 16518 |
\begin{align*}
y^{\prime }+y \cot \left (x \right )&=\csc \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.371 |
|
| 16519 |
\begin{align*}
x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.372 |
|
| 16520 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.373 |
|
| 16521 |
\begin{align*}
y^{\prime }-y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.373 |
|
| 16522 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.374 |
|
| 16523 |
\begin{align*}
x^{2} y^{\prime \prime }&=\sqrt {m \,x^{2} {y^{\prime }}^{3}+n y^{2}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.374 |
|
| 16524 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+a +y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.375 |
|
| 16525 |
\begin{align*}
-12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime }&=1+3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.376 |
|
| 16526 |
\begin{align*}
y^{\prime }&=\frac {2 y^{2}}{x}+\frac {y}{x}-2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.376 |
|
| 16527 |
\begin{align*}
3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.376 |
|
| 16528 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.377 |
|
| 16529 |
\begin{align*}
y^{\prime }&=\ln \left (-1+y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.378 |
|
| 16530 |
\begin{align*}
x y^{\prime }-y-\frac {x}{\ln \left (x \right )}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.379 |
|
| 16531 |
\begin{align*}
y^{\prime }-y x&=\left (-x^{2}+1\right ) {\mathrm e}^{\frac {x^{2}}{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.380 |
|
| 16532 |
\begin{align*}
b x y+a y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.381 |
|
| 16533 |
\begin{align*}
2 x^{2} y+x^{3} y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.382 |
|
| 16534 |
\begin{align*}
x^{2} y^{\prime \prime }+5 x y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.382 |
|
| 16535 |
\begin{align*}
-2 \left (-3 x +1\right ) y-x \left (1-4 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=x^{3} \left (x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.382 |
|
| 16536 |
\begin{align*}
x^{\prime } t +x g \left (t \right )&=h \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.384 |
|
| 16537 |
\begin{align*}
2 y t +\left (t^{2}+3 y^{2}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.384 |
|
| 16538 |
\begin{align*}
y^{\prime }&={\mathrm e}^{4 x +3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.385 |
|
| 16539 |
\begin{align*}
\left (x -y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.385 |
|
| 16540 |
\begin{align*}
s^{2} t^{\prime \prime }+s t t^{\prime }&=s \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.386 |
|
| 16541 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.386 |
|
| 16542 |
\begin{align*}
x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.387 |
|
| 16543 |
\begin{align*}
y^{\prime }+\frac {3 y}{x}+2&=3 x \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.387 |
|
| 16544 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= {\mathrm e}^{-2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.387 |
|
| 16545 |
\begin{align*}
y^{\prime }&=2 x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.388 |
|
| 16546 |
\begin{align*}
y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 \csc \left (x \right )^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.388 |
|
| 16547 |
\begin{align*}
y^{\prime \prime }&=\sqrt {2 x +1} \\
y \left (0\right ) &= 5 \\
y \left (4\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.388 |
|
| 16548 |
\begin{align*}
x^{\prime }-\frac {x}{t -1}&=t^{2}+2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.389 |
|
| 16549 |
\begin{align*}
x^{\prime }&=-4 x+y-t +3 \\
y^{\prime }&=-x-5 y+t +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.389 |
|
| 16550 |
\begin{align*}
x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=x^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.389 |
|
| 16551 |
\begin{align*}
3 x^{2} \left (1+\ln \left (y\right )\right )&=\left (2 y-\frac {x^{3}}{y}\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.389 |
|
| 16552 |
\begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.390 |
|
| 16553 |
\begin{align*}
y^{\prime }&=\frac {y x}{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.390 |
|
| 16554 |
\begin{align*}
x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y&=\frac {1}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.391 |
|
| 16555 |
\begin{align*}
-\frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\
y \left (0\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.392 |
|
| 16556 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+a -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.392 |
|
| 16557 |
\begin{align*}
y^{\prime }-y&={\mathrm e}^{2 x} y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.392 |
|
| 16558 |
\begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= \operatorname {yd}_{0} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.392 |
|
| 16559 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+8 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.392 |
|
| 16560 |
\begin{align*}
\left (y^{2}-x \right ) y^{\prime }-y+x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.393 |
|
| 16561 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.394 |
|
| 16562 |
\begin{align*}
x^{2}-2 y+x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.394 |
|
| 16563 |
\begin{align*}
\tan \left (t \right ) y+y^{\prime }&=\sin \left (t \right ) \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.395 |
|
| 16564 |
\begin{align*}
x^{2} y^{\prime }+y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.395 |
|
| 16565 |
\begin{align*}
-y+x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=x \left (-x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.395 |
|
| 16566 |
\begin{align*}
y^{\prime \prime }-25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.396 |
|
| 16567 |
\begin{align*}
t \ln \left (t \right ) y^{\prime }&=t \ln \left (t \right )-y \\
y \left ({\mathrm e}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.397 |
|
| 16568 |
\begin{align*}
y^{\prime }&=2 y x -x^{3}+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.397 |
|
| 16569 |
\begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.398 |
|
| 16570 |
\begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.398 |
|
| 16571 |
\begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.398 |
|
| 16572 |
\begin{align*}
y^{\prime }&=-y^{2} {\mathrm e}^{-x}+y+{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.398 |
|
| 16573 |
\begin{align*}
y+y^{\prime }&=t^{3}+\sin \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.400 |
|
| 16574 |
\begin{align*}
\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.400 |
|
| 16575 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=x^{2} {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.401 |
|
| 16576 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.401 |
|
| 16577 |
\begin{align*}
y^{\prime }+y \tan \left (x \right )-\sin \left (2 x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.401 |
|
| 16578 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.402 |
|
| 16579 |
\begin{align*}
y^{\prime }+x^{2} y&=\left (x^{2}+1\right ) {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.402 |
|
| 16580 |
\begin{align*}
y^{\prime }-y \tan \left (x \right )&=1 \\
y \left (\frac {\pi }{4}\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.403 |
|
| 16581 |
\begin{align*}
y^{\prime \prime \prime }-a^{2} \left ({y^{\prime }}^{5}+2 {y^{\prime }}^{3}+y^{\prime }\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.403 |
|
| 16582 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.404 |
|
| 16583 |
\begin{align*}
x y^{\prime }+3 x^{2}+3 y&=\frac {\sin \left (x \right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.404 |
|
| 16584 |
\begin{align*}
p \left (1+p \right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✓ |
2.404 |
|
| 16585 |
\begin{align*}
\left (a \,x^{2}+2 b x +c \right ) y^{\prime \prime }+3 \left (a x +b \right ) y^{\prime }+d y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.404 |
|
| 16586 |
\begin{align*}
x y^{\prime }-y&=2 x^{2}-3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.404 |
|
| 16587 |
\begin{align*}
y^{\prime }&=\left (x -y\right )^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.404 |
|
| 16588 |
\begin{align*}
\left (t^{3}-2 t^{2}\right ) x^{\prime \prime }-\left (t^{3}+2 t^{2}-6 t \right ) x^{\prime }+\left (3 t^{2}-6\right ) x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.405 |
|
| 16589 |
\begin{align*}
x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.405 |
|
| 16590 |
\begin{align*}
{y^{\prime }}^{2}&=1-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.406 |
|
| 16591 |
\begin{align*}
y+y^{\prime }&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.406 |
|
| 16592 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-4 x_{2}+5 x_{3}+9 x_{4} \\
x_{2}^{\prime }&=-2 x_{1}-5 x_{2}+4 x_{3}+12 x_{4} \\
x_{3}^{\prime }&=-2 x_{1}-x_{3}+2 x_{4} \\
x_{4}^{\prime }&=-2 x_{2}+2 x_{3}+3 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.406 |
|
| 16593 |
\begin{align*}
x y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }+x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.408 |
|
| 16594 |
\begin{align*}
y^{\prime }-a y&={\mathrm e}^{a x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.408 |
|
| 16595 |
\begin{align*}
\left (1+{\mathrm e}^{x}\right ) y y^{\prime }&={\mathrm e}^{y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.408 |
|
| 16596 |
\begin{align*}
y^{\prime }&=1+x +y+y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.412 |
|
| 16597 |
\begin{align*}
y^{\prime \prime }&=-\frac {2 y^{\prime }}{x}-\frac {a^{2} y}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.412 |
|
| 16598 |
\begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.413 |
|
| 16599 |
\begin{align*}
y^{\prime }&=t +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.413 |
|
| 16600 |
\begin{align*}
\left (2 x -1\right ) y^{\prime }-2 y&=\frac {1-4 x}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.413 |
|