| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 5401 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2}+2 x_{3}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}+3 x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.361 |
|
| 5402 |
\begin{align*}
x_{1}^{\prime }&=4 x_{2} \\
x_{2}^{\prime }&=-9 x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| 5403 |
\begin{align*}
2 x +\cos \left (x \right ) y+\left (2 y+\sin \left (x \right )-\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.361 |
|
| 5404 |
\begin{align*}
{y^{\prime }}^{3} x -\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| 5405 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.361 |
|
| 5406 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| 5407 |
\begin{align*}
4 x^{\prime \prime }-20 x^{\prime }+21 x&=0 \\
x \left (0\right ) &= -4 \\
x^{\prime }\left (0\right ) &= -12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| 5408 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| 5409 |
\begin{align*}
y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| 5410 |
\begin{align*}
u^{\prime \prime }-\left (x +1\right ) u^{\prime }+\left (x -1\right ) u&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.361 |
|
| 5411 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-12 y&={\mathrm e}^{x} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| 5412 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=12 t \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| 5413 |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }+25 y&=100 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 20 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| 5414 |
\begin{align*}
y^{\prime \prime }-\left (1+\frac {3}{2 x}\right ) y^{\prime }+\frac {3 y}{2 x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| 5415 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| 5416 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| 5417 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| 5418 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&={\mathrm e}^{t}+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| 5419 |
\begin{align*}
x^{2} y^{\prime \prime \prime }&=2 y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| 5420 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-4 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+9 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5421 |
\begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5422 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=8 x_{1}-4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5423 |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-y^{\prime } t +\alpha ^{2} y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5424 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5425 |
\begin{align*}
y^{\prime } x&=-\sqrt {a^{2}-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5426 |
\begin{align*}
-\left (2 x^{2}+1\right ) y+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5427 |
\begin{align*}
a y^{\prime } \left (-y+y^{\prime } x \right )+x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.362 |
|
| 5428 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5429 |
\begin{align*}
t^{2} y^{\prime \prime }-2 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5430 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime } x +\left (2 x^{2}+5\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.362 |
|
| 5431 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.362 |
|
| 5432 |
\begin{align*}
x^{\prime }&=4 y \\
y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5433 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=0 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5434 |
\begin{align*}
y^{\prime }&=\left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x <2 \\ 0 & 2\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5435 |
\begin{align*}
y^{\prime }-{\mathrm e}^{2 x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5436 |
\begin{align*}
x^{2} y^{\prime \prime }&=2 y^{\prime } x +{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5437 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5438 |
\begin{align*}
x^{\prime \prime }-4 x^{\prime }+4 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5439 |
\begin{align*}
{y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 y^{2} y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5440 |
\begin{align*}
x^{2} y^{\prime \prime \prime }-2 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5441 |
\begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5442 |
\begin{align*}
3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5443 |
\begin{align*}
x^{\prime }-x+2 y^{\prime }+7 y&=0 \\
2 x^{\prime }+y^{\prime }+x+5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5444 |
\begin{align*}
x^{\prime \prime }-2 x^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5445 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5446 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5447 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5448 |
\begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } x&=8 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| 5449 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=6 x+3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.363 |
|
| 5450 |
\begin{align*}
x^{\prime \prime }+9 x&=\delta \left (t -3 \pi \right )+\cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| 5451 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| 5452 |
\begin{align*}
4 \left (-x +2\right ) {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| 5453 |
\begin{align*}
y^{\prime }&=\left (-2+y\right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| 5454 |
\begin{align*}
x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| 5455 |
\begin{align*}
x^{2} y^{\prime \prime \prime }+5 y^{\prime \prime } x +4 y^{\prime }-\ln \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| 5456 |
\begin{align*}
y^{\prime }-y&=2 \,{\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| 5457 |
\begin{align*}
y^{\prime \prime \prime \prime }-16 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
y^{\prime \prime }\left (0\right ) &= 4 \\
y^{\prime \prime \prime }\left (0\right ) &= -24 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| 5458 |
\begin{align*}
x^{\prime }&=3 x+6 y \\
y^{\prime }&=-x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| 5459 |
\begin{align*}
2 y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| 5460 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| 5461 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| 5462 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| 5463 |
\begin{align*}
y^{\prime \prime }+y&=\sqrt {2}\, \sin \left (\sqrt {2}\, t \right ) \\
y \left (0\right ) &= 10 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| 5464 |
\begin{align*}
\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.364 |
|
| 5465 |
\begin{align*}
5 y^{\prime \prime }-2 y^{\prime } x +10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.364 |
|
| 5466 |
\begin{align*}
y^{\prime \prime }-2 k y^{\prime }+k^{2} y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| 5467 |
\begin{align*}
x^{\prime }&=-9 y \\
y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| 5468 |
\begin{align*}
x^{\prime }&=8 y-x \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| 5469 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| 5470 |
\begin{align*}
y^{\prime \prime \prime }&=\sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| 5471 |
\begin{align*}
y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&={\mathrm e}^{2 x} \cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| 5472 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{x} \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| 5473 |
\begin{align*}
x^{\prime }&=-2 y \\
y^{\prime }&=2 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5474 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
y \left (0\right ) &= \alpha \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5475 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5476 |
\begin{align*}
\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y&=\left (2 x +1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.365 |
|
| 5477 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5478 |
\begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5479 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=2 \cos \left (t \right )^{2} {\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5480 |
\begin{align*}
y^{\prime \prime }+4 y&=10 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5481 |
\begin{align*}
a \cos \left (y^{\prime }\right )+b y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.365 |
|
| 5482 |
\begin{align*}
2 \,{\mathrm e}^{2 x} y+2 x \cos \left (y\right )+\left ({\mathrm e}^{2 x}-x^{2} \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.365 |
|
| 5483 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+y&=3 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5484 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5485 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.365 |
|
| 5486 |
\begin{align*}
y^{\prime \prime }&=\left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.365 |
|
| 5487 |
\begin{align*}
y^{\prime }+y f^{\prime }\left (x \right )-f \left (x \right ) f^{\prime }\left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5488 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5489 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\frac {y^{\prime }}{y}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.365 |
|
| 5490 |
\begin{align*}
y^{\prime \prime }-\sin \left (x \right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5491 |
\begin{align*}
y^{\prime }&=x -y \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5492 |
\begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-2 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= a \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5493 |
\begin{align*}
{y^{\prime \prime }}^{{3}/{2}}+y&=x \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.365 |
|
| 5494 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=4 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5495 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }-5 y&={\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5496 |
\begin{align*}
y^{\prime \prime }+10 y^{\prime }+25 y&=2 \,{\mathrm e}^{-5 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5497 |
\begin{align*}
y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5498 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5499 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-15 y&=16 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| 5500 |
\begin{align*}
y_{1}^{\prime }-3 y_{1}&=-4 y_{2} \\
y_{2}^{\prime }+y_{2}&=y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|