| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 9401 |
\begin{align*}
2 x +3 y+4+\left (3 x +4 y+5\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| 9402 |
\begin{align*}
{y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.477 |
|
| 9403 |
\begin{align*}
y^{\prime \prime \prime }&=x^{2}+{\mathrm e}^{-x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| 9404 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=5 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| 9405 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y&=x \,{\mathrm e}^{x} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.477 |
|
| 9406 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-24 y&=16-\left (2+x \right ) {\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| 9407 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| 9408 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-1+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| 9409 |
\begin{align*}
x^{\prime }&=-3 x+y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| 9410 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=-18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| 9411 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=-4 \cos \left (x \right )+7 \sin \left (x \right ) \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| 9412 |
\begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| 9413 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (\sin \left (2 x \right )-\cos \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| 9414 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+4 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=3 x_{2}+2 x_{3} \\
x_{3}^{\prime }&=2 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| 9415 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime \prime }-y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.477 |
|
| 9416 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 y^{\prime } x&=\ln \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| 9417 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-4 x^{2}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| 9418 | \begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right )^{2} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.478 |
|
| 9419 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}-x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| 9420 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}-x_{2}+4 x_{3} \\
x_{2}^{\prime }&=-x_{2} \\
x_{3}^{\prime }&=-x_{1}-3 x_{2}+2 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -2 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| 9421 |
\begin{align*}
4 y+y^{\prime \prime }&=8 \sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| 9422 |
\begin{align*}
2 y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.478 |
|
| 9423 |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=\sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| 9424 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\sin \left ({\mathrm e}^{-x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| 9425 |
\begin{align*}
y^{\prime }&=k y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| 9426 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 x+2 y-z \\
z^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| 9427 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y x&=\cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.478 |
|
| 9428 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+20 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| 9429 |
\begin{align*}
x^{\prime \prime }-2 x^{\prime }+5 x&=0 \\
x \left (0\right ) &= 0 \\
x \left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| 9430 |
\begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=9 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| 9431 |
\begin{align*}
\left (x +4\right ) y^{\prime \prime }-\left (4+2 x \right ) y^{\prime }+\left (6+x \right ) y&=0 \\
y \left (-3\right ) &= 2 \\
y^{\prime }\left (-3\right ) &= -2 \\
\end{align*} Series expansion around \(x=-3\). |
✓ |
✓ |
✓ |
✓ |
0.479 |
|
| 9432 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.479 |
|
| 9433 |
\begin{align*}
-{y^{\prime }}^{2}+4 y {y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.479 |
|
| 9434 |
\begin{align*}
y^{\prime \prime }&=\frac {\left (1+3 x \right ) y^{\prime }}{\left (x -1\right ) \left (x +1\right )}-\frac {36 \left (x +1\right )^{2} y}{\left (x -1\right )^{2} \left (3 x +5\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.479 |
|
| 9435 |
\begin{align*}
y^{\prime \prime }+\left (5+2 x \right ) y^{\prime }+\left (4 x +8\right ) y&={\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.479 |
|
| 9436 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right )-\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.479 |
|
| 9437 | \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=\cosh \left (2 t \right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 0.479 |
|
| 9438 |
\begin{align*}
y^{\prime }&=2 y x \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.479 |
|
| 9439 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.479 |
|
| 9440 |
\begin{align*}
y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| 9441 |
\begin{align*}
y^{\prime \prime } x +\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.480 |
|
| 9442 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| 9443 |
\begin{align*}
y^{\prime \prime }-4 y&=x +{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| 9444 |
\begin{align*}
x_{1}^{\prime }&=15 x_{1}-32 x_{2}+12 x_{3} \\
x_{2}^{\prime }&=8 x_{1}-17 x_{2}+6 x_{3} \\
x_{3}^{\prime }&=-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| 9445 |
\begin{align*}
x_{1}^{\prime }&=-17 x_{1}-42 x_{3} \\
x_{2}^{\prime }&=-7 x_{1}+4 x_{2}-14 x_{3} \\
x_{3}^{\prime }&=7 x_{1}+18 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| 9446 |
\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. |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| 9447 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| 9448 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime } y+{\mathrm e}^{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.480 |
|
| 9449 |
\begin{align*}
y a^{2} x^{2}-2 a x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.480 |
|
| 9450 |
\begin{align*}
u^{\prime }-u^{2}&=\frac {2}{x^{{8}/{3}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.480 |
|
| 9451 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x -x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.480 |
|
| 9452 |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{x} \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.480 |
|
| 9453 |
\begin{align*}
t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.480 |
|
| 9454 |
\begin{align*}
x^{\prime }&=3 x+y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| 9455 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+8 y&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| 9456 | \begin{align*}
x^{2} y^{\prime \prime }+\left (-x^{4}+x \right ) y^{\prime }+3 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.480 |
|
| 9457 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| 9458 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=4 \cos \left (2 x \right )+\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| 9459 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (1\right ) &= {\mathrm e}^{2} \\
y^{\prime }\left (1\right ) &= 3 \,{\mathrm e}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| 9460 |
\begin{align*}
y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5}&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.480 |
|
| 9461 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| 9462 |
\begin{align*}
x^{\prime }&=2 x+6 y \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| 9463 |
\begin{align*}
y^{\prime \prime }+y&=2 \cos \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| 9464 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}-3 \,{\mathrm e}^{t} \\
x_{2}^{\prime }&=-2 x_{1}-x_{2}+6 \,{\mathrm e}^{t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| 9465 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=15 \,{\mathrm e}^{-x} \sqrt {x +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| 9466 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| 9467 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
y \left (1\right ) &= -6 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| 9468 |
\begin{align*}
y+y^{\prime }&=\delta \left (-1+t \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| 9469 |
\begin{align*}
\left (1+y\right ) y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.481 |
|
| 9470 |
\begin{align*}
y^{\prime \prime }&=\frac {2 \left (a x +2 b \right ) y^{\prime }}{x \left (a x +b \right )}-\frac {\left (2 a x +6 b \right ) y}{\left (a x +b \right ) x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.481 |
|
| 9471 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+13 y&=25 \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| 9472 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=3 \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| 9473 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (2 x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| 9474 |
\begin{align*}
x^{\prime }+x-5 y&=0 \\
y^{\prime }+4 x+5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| 9475 | \begin{align*}
p^{\prime }&=p \left (1-p\right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.481 |
|
| 9476 |
\begin{align*}
x_{1}^{\prime }&=-\frac {x_{1}}{10}+\frac {3 x_{2}}{40} \\
x_{2}^{\prime }&=\frac {x_{1}}{10}-\frac {x_{2}}{5} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -17 \\
x_{2} \left (0\right ) &= -21 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| 9477 |
\begin{align*}
\left (x +1\right ) y^{\prime \prime }+2 \left (x -1\right )^{2} y^{\prime }+3 y&=0 \\
y \left (1\right ) &= a_{0} \\
y^{\prime }\left (1\right ) &= a_{1} \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| 9478 |
\begin{align*}
x_{1}^{\prime }&=-7 x_{1}-6 x_{2}-7 x_{3} \\
x_{2}^{\prime }&=-3 x_{1}-3 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=7 x_{1}+6 x_{2}+7 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| 9479 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=9 x^{2}+4 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| 9480 |
\begin{align*}
y^{\prime \prime }+\left (6 x^{2}+2 x +1\right ) y^{\prime }+\left (2+12 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| 9481 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=2 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| 9482 |
\begin{align*}
x^{\prime \prime }-6 x^{\prime }+9 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| 9483 |
\begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=-3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| 9484 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| 9485 |
\begin{align*}
\left (x +1\right ) y^{\prime \prime }+3 y^{\prime }-2 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| 9486 |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y \left (\pi \right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| 9487 |
\begin{align*}
y^{\prime }&=a \left (t \right ) y+\delta \left (-t +s \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| 9488 |
\begin{align*}
4 y+y^{\prime \prime }&=2 x \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| 9489 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=\delta \left (-1+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| 9490 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -2 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| 9491 |
\begin{align*}
y^{\prime \prime }+t y^{\prime }+y \,{\mathrm e}^{t}&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| 9492 |
\begin{align*}
y^{\prime \prime }+4 y&=\sin \left (t \right )+\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| 9493 |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{2 x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| 9494 | \begin{align*}
9 y+6 y^{\prime }+y^{\prime \prime }&=\cosh \left (x \right ) {\mathrm e}^{-3 x} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.483 |
|
| 9495 |
\begin{align*}
-\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.483 |
|
| 9496 |
\begin{align*}
{\mathrm e}^{x} \left (y^{3}+x y^{3}+1\right )+3 y^{2} \left (x \,{\mathrm e}^{x}-6\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| 9497 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=3 \sin \left (x \right ) \\
y \left (0\right ) &= -{\frac {9}{10}} \\
y^{\prime }\left (0\right ) &= -{\frac {7}{10}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| 9498 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 \left (x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| 9499 |
\begin{align*}
y^{\prime \prime }+\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+f \left (x \right ) y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.483 |
|
| 9500 |
\begin{align*}
x^{\prime }+5 x&=\operatorname {Heaviside}\left (t -2\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.483 |
|