| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15501 |
\begin{align*}
y^{\prime }+f \left (x \right )^{2}&=f^{\prime }\left (x \right )+y^{2} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.316 |
|
| 15502 |
\begin{align*}
{y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.316 |
|
| 15503 |
\begin{align*}
3 x^{2} y^{\prime \prime }-2 y^{\prime } x -8 y&=3 x +5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.316 |
|
| 15504 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 6 & 1\le t <3 \\ 0 & 3\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.316 |
|
| 15505 |
\begin{align*}
\left (y^{3}+1\right ) y^{\prime }&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.317 |
|
| 15506 |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}+\left (a y+b \right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.317 |
|
| 15507 |
\begin{align*}
y^{\prime }&=\frac {y+x^{2}}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.317 |
|
| 15508 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.318 |
|
| 15509 |
\begin{align*}
\left (1-2 y\right ) {y^{\prime }}^{2}+\left (1+y^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.319 |
|
| 15510 |
\begin{align*}
y^{\prime \prime }&={\mathrm e}^{y} y^{\prime } \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.319 |
|
| 15511 |
\begin{align*}
y^{\prime }&=y^{3}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.319 |
|
| 15512 |
\begin{align*}
L i^{\prime }+R i&=E \\
i \left (0\right ) &= i_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.320 |
|
| 15513 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=\operatorname {Heaviside}\left (-1+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.320 |
|
| 15514 |
\begin{align*}
y^{\prime }&=\frac {1}{2 x -y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.320 |
|
| 15515 |
\begin{align*}
y^{\prime \prime }+3 y&=\sin \left (x \right )+\frac {\sin \left (3 x \right )}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.320 |
|
| 15516 |
\begin{align*}
y^{\prime }&=\frac {y x +2 y}{x} \\
y \left (1\right ) &= {\mathrm e} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.320 |
|
| 15517 |
\begin{align*}
\frac {c y^{\prime \prime }}{\omega ^{2}}+c y&=\cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.320 |
|
| 15518 | \begin{align*}
\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right )&=x \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 1.321 |
|
| 15519 |
\begin{align*}
\left (x +1\right ) \left (2 x +3\right ) y^{\prime \prime }+2 \left (2+x \right ) y^{\prime }-2 y&=\left (2 x +3\right )^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.322 |
|
| 15520 |
\begin{align*}
y^{\prime }&=1+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| 15521 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| 15522 |
\begin{align*}
\left (x +1\right )^{3} y^{\prime \prime }+3 \left (x +1\right )^{2} y^{\prime }+\left (x +1\right ) y&=6 \ln \left (x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.323 |
|
| 15523 |
\begin{align*}
y^{\prime }&=\frac {x +2 y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.323 |
|
| 15524 |
\begin{align*}
-y+y^{\prime }&=2 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.325 |
|
| 15525 |
\begin{align*}
y^{\left (6\right )}-2 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+3 y^{\prime \prime }-2 y^{\prime }+y&=\sin \left (\frac {x}{2}\right )^{2}+{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.325 |
|
| 15526 |
\begin{align*}
y^{\prime }&=2 \sqrt {2 x +y-3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.326 |
|
| 15527 |
\begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.326 |
|
| 15528 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -2 y&=x^{2}-2 x +2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.326 |
|
| 15529 |
\begin{align*}
x^{\prime }&=2 x+y-2 z+2-t \\
y^{\prime }&=1-x \\
z^{\prime }&=x+y-z+1-t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.326 |
|
| 15530 |
\begin{align*}
\frac {y}{x}+\ln \left (x \right ) y^{\prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.326 |
|
| 15531 |
\begin{align*}
-2 y+3 y^{\prime }&={\mathrm e}^{-\frac {\pi t}{2}} \\
y \left (0\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.327 |
|
| 15532 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=2 x \left (x -y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.327 |
|
| 15533 |
\begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.327 |
|
| 15534 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-x^{2}+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.328 |
|
| 15535 |
\begin{align*}
{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.328 |
|
| 15536 |
\begin{align*}
5 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.328 |
|
| 15537 | \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +5 y&=0 \\
y \left (1\right ) &= \sqrt {2} \\
y^{\prime }\left (1\right ) &= 3 \sqrt {2} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.329 |
|
| 15538 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+x^{2}+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.329 |
|
| 15539 |
\begin{align*}
y^{2} {y^{\prime }}^{3}-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.329 |
|
| 15540 |
\begin{align*}
x^{\prime }&=-7 x+10 y+18 \,{\mathrm e}^{t} \\
y^{\prime }&=-10 x+9 y+37 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.329 |
|
| 15541 |
\begin{align*}
y^{\prime }&=1+y x +3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.329 |
|
| 15542 |
\begin{align*}
-y+y^{\prime }&=4 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.329 |
|
| 15543 |
\begin{align*}
y^{\prime }-a \left (t \right ) y&=q \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.329 |
|
| 15544 |
\begin{align*}
x^{\prime }&=3 y-3 x \\
y^{\prime }&=x+2 y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.331 |
|
| 15545 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.331 |
|
| 15546 |
\begin{align*}
y^{\prime }-3 z&=5 \\
y-z^{\prime }-x&=3-2 t \\
z+x^{\prime }&=-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.331 |
|
| 15547 |
\begin{align*}
y^{\prime }&=y-{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.331 |
|
| 15548 |
\begin{align*}
y^{\prime }&=\left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.332 |
|
| 15549 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.332 |
|
| 15550 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.332 |
|
| 15551 |
\begin{align*}
x^{\prime }&=3 x-2 y+2 t^{2} \\
y^{\prime }&=5 x+y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.332 |
|
| 15552 |
\begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.332 |
|
| 15553 |
\begin{align*}
-5 y-3 y^{\prime } x +x^{2} y^{\prime \prime }&=\ln \left (x \right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.333 |
|
| 15554 |
\begin{align*}
v^{\prime }&=-\frac {v}{R C} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.333 |
|
| 15555 |
\begin{align*}
y^{\prime }&=-y-\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.334 |
|
| 15556 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2 c}+b \,x^{c -1}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.334 |
|
| 15557 | \begin{align*}
2 y y^{\prime \prime }-6 {y^{\prime }}^{2}+y^{2} \left (1+a y^{3}\right )&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 1.334 |
|
| 15558 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.334 |
|
| 15559 |
\begin{align*}
y^{\prime }&=-t y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.334 |
|
| 15560 |
\begin{align*}
y^{\prime } x +x +\left (a x +2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| 15561 |
\begin{align*}
-y+y^{\prime } x&=y^{2}+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| 15562 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| 15563 |
\begin{align*}
y+2 y^{\prime }&=3 t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| 15564 |
\begin{align*}
y^{\prime }+2 y x&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| 15565 |
\begin{align*}
2 y^{3} y^{\prime }&=x^{3}-x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.336 |
|
| 15566 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x -\left (a \,x^{n}-a b \,x^{n -1}+b \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.336 |
|
| 15567 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (2\right ) &= 4 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| 15568 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&=3 t +2 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| 15569 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| 15570 |
\begin{align*}
y^{\prime }+10 y&=2 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| 15571 |
\begin{align*}
y-\left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.337 |
|
| 15572 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{2 x}+b \,{\mathrm e}^{x}+c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.337 |
|
| 15573 |
\begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x -5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.337 |
|
| 15574 |
\begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| 15575 |
\begin{align*}
x^{2}+y+y^{2}-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| 15576 |
\begin{align*}
4 x {y^{\prime }}^{2}&=\left (a -3 x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| 15577 | \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=x^{3} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.339 |
|
| 15578 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\frac {y}{4}&=-\frac {x^{2}}{2}+\frac {1}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.339 |
|
| 15579 |
\begin{align*}
y^{\prime \prime } x -\left (x^{2}-x -2\right ) y^{\prime }-x \left (x +3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.339 |
|
| 15580 |
\begin{align*}
y^{\prime \prime }-6 y^{2}+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.339 |
|
| 15581 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=2 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| 15582 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| 15583 |
\begin{align*}
y^{\prime \prime }+9 y&=18 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| 15584 |
\begin{align*}
-\left (\left (2 n +1\right )^{2}-4 x^{2}\right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.340 |
|
| 15585 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=\sec \left (a x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.340 |
|
| 15586 |
\begin{align*}
y^{\prime }&={\mathrm e}^{3+t +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| 15587 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }-a +y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| 15588 |
\begin{align*}
y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}+b -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 \mu x}+d \,{\mathrm e}^{\mu x}+k \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
1.342 |
|
| 15589 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.342 |
|
| 15590 |
\begin{align*}
x^{2} \cos \left (x \right ) y^{\prime \prime }+\left (x \sin \left (x \right )-2 \cos \left (x \right )\right ) \left (-y+y^{\prime } x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.342 |
|
| 15591 |
\begin{align*}
{\mathrm e}^{x}-y^{\prime } y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| 15592 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=6 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 11 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.343 |
|
| 15593 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+2 x_{3} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
x_{3}^{\prime }&=-2 x_{1}-x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= -1 \\
x_{3} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.343 |
|
| 15594 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +p^{2} y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.343 |
|
| 15595 |
\begin{align*}
y^{\prime \prime }&=x^{2} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.343 |
|
| 15596 | \begin{align*}
y^{\prime \prime }+\left (1-\frac {3}{4 x^{2}}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 1.344 |
|
| 15597 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}-2 x \right ) y^{\prime }-\left (3 x +2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.344 |
|
| 15598 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.344 |
|
| 15599 |
\begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.344 |
|
| 15600 |
\begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.344 |
|