| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 6401 |
\begin{align*}
z^{\prime \prime }-4 z&=\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| 6402 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+56 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| 6403 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=12 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| 6404 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=x^{2} {\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| 6405 |
\begin{align*}
2 y^{\prime \prime }+4 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.487 |
|
| 6406 |
\begin{align*}
y^{\prime }-2 y x&=0 \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| 6407 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2} \\
x_{2}^{\prime }&=-6 x_{1} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -19 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| 6408 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}+1 \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+3 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| 6409 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| 6410 |
\begin{align*}
y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| 6411 |
\begin{align*}
x^{\prime }&=6 x-3 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| 6412 |
\begin{align*}
y^{\prime \prime \prime }&=1+\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| 6413 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{x} \left (1-x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| 6414 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{t} \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| 6415 |
\begin{align*}
y^{\prime \prime }-2 y^{3}-y x +a&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.488 |
|
| 6416 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2}-x^{2} y^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.488 |
|
| 6417 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{-x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| 6418 |
\begin{align*}
\left (-x^{3}+2\right ) y^{\prime }-3 x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| 6419 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=5 x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 15 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| 6420 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| 6421 |
\begin{align*}
{y^{\prime }}^{3}+2 {y^{\prime }}^{2} x -y^{2} {y^{\prime }}^{2}-2 x y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| 6422 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+5 y&=4 \,{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| 6423 |
\begin{align*}
\left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.488 |
|
| 6424 |
\begin{align*}
\left (1-x \right )^{2} y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| 6425 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| 6426 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+x_{3} \\
x_{2}^{\prime }&=-x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}-x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| 6427 |
\begin{align*}
\left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| 6428 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| 6429 |
\begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=5 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| 6430 |
\begin{align*}
\left (1-x \right ) y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=5\). |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| 6431 |
\begin{align*}
y^{\prime }&=x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| 6432 |
\begin{align*}
y^{\prime \prime }-y&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| 6433 |
\begin{align*}
x^{2} \ln \left (x \right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.489 |
|
| 6434 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2} \\
x_{2}^{\prime }&=-2 x_{1}+x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 11 \\
x_{2} \left (0\right ) &= -7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6435 |
\begin{align*}
y_{1}^{\prime }&=-11 y_{1}+8 y_{2} \\
y_{2}^{\prime }&=-2 y_{1}-3 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 6 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6436 |
\begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }&={\mathrm e}^{-2 x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6437 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6438 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6439 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }+p x y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6440 |
\begin{align*}
y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6441 |
\begin{align*}
2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.490 |
|
| 6442 |
\begin{align*}
2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.490 |
|
| 6443 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&=-\cos \left (5 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6444 |
\begin{align*}
2 x^{\prime \prime }-2 x^{\prime }&=\left (t +1\right ) {\mathrm e}^{t} \\
x \left (0\right ) &= {\frac {1}{2}} \\
x^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6445 |
\begin{align*}
y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6446 |
\begin{align*}
x^{2} y^{\prime \prime \prime }-x y^{\prime \prime }+y^{\prime }&=\frac {\ln \left (x \right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6447 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6448 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=-6 x^{2}-8 x +4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6449 |
\begin{align*}
y^{\prime \prime }-y&=16 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6450 |
\begin{align*}
4 y^{\prime \prime }-y&=x +{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6451 |
\begin{align*}
y_{1}^{\prime }&=3 y_{1}-4 y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6452 |
\begin{align*}
-x y^{\prime }+y&={y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.490 |
|
| 6453 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| 6454 |
\begin{align*}
x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.490 |
|
| 6455 |
\begin{align*}
y^{\prime \prime }+{\mathrm e}^{-x} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 6456 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2} \\
x_{2}^{\prime }&=-4 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 6457 |
\begin{align*}
y^{\prime }&=\frac {t}{\sqrt {t}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 6458 |
\begin{align*}
x^{\prime }-x-2 y&=16 \,{\mathrm e}^{t} t \\
2 x-y^{\prime }-2 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 6459 |
\begin{align*}
{y^{\prime }}^{2} x^{2}-5 x y y^{\prime }+6 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 6460 |
\begin{align*}
y^{\prime \prime }+9 y&=5 \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 6461 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 6462 |
\begin{align*}
x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2}-3 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.491 |
|
| 6463 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 6464 |
\begin{align*}
y^{\prime }-3 y&=13 \cos \left (2 t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 6465 |
\begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-\left (x^{2}-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 6466 |
\begin{align*}
{y^{\prime }}^{2} x +\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 6467 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| 6468 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=-7 x_{1}+9 x_{2}+7 x_{3} \\
x_{3}^{\prime }&=2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 6469 |
\begin{align*}
-\left (a^{2}-b \,{\mathrm e}^{x}\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.492 |
|
| 6470 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 6471 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+25 y&=64 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 6472 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 6473 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 6474 |
\(\left [\begin {array}{cc} 3 & 1 \\ 12 & 2 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.492 |
|
| 6475 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+34 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 6476 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \delta \left (x -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 6477 |
\begin{align*}
x^{\prime }&=5 x+4 y \\
y^{\prime }&=8 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 6478 |
\begin{align*}
y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 6479 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 6480 |
\begin{align*}
x y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\
y \left (3\right ) &= 2 \\
y^{\prime }\left (3\right ) &= 0 \\
\end{align*}
Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 6481 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=20 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 6482 |
\begin{align*}
y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 6483 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\left (x^{2}+x \right ) {\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| 6484 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=3 x_{1}+2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 6485 |
\begin{align*}
2 x^{\prime \prime }+2 x^{\prime }+x&=3 \sin \left (10 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 6486 |
\begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=16 \,{\mathrm e}^{\frac {t}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 6487 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-3 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}+2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 6488 |
\begin{align*}
4 y+y^{\prime \prime }&=x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 6489 |
\begin{align*}
{y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 6490 |
\begin{align*}
12 y-7 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 6491 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{i x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 6492 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 6493 |
\begin{align*}
y^{\prime \prime }+y&=2 x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 6494 |
\begin{align*}
2 y-x y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.493 |
|
| 6495 |
\begin{align*}
x y^{\prime \prime }+x y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.493 |
|
| 6496 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 6497 |
\begin{align*}
y_{1}^{\prime }&=y_{1} \\
y_{2}^{\prime }&=y_{1}+y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 6498 |
\begin{align*}
f \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| 6499 |
\begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }-9 x y^{\prime }-6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.493 |
|
| 6500 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=4 \,{\mathrm e}^{x}-18 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|