| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 6401 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 6402 |
\begin{align*}
y^{\prime }&=1+3 x \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 6403 |
\begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| 6404 |
\begin{align*}
y^{\prime \prime }&=x y^{2}-y^{\prime } \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.800 |
|
| 6405 |
\begin{align*}
x_{1}^{\prime }&=-\frac {x_{1}}{4}+x_{2} \\
x_{2}^{\prime }&=-x_{1}-\frac {x_{2}}{4} \\
x_{3}^{\prime }&=\frac {x_{3}}{10} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| 6406 |
\begin{align*}
4 y+y^{\prime \prime }&=2 x -2 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| 6407 |
\begin{align*}
y^{\prime }+\sin \left (x \right ) y^{2}-\frac {2 \sin \left (x \right )}{\cos \left (x \right )^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.801 |
|
| 6408 |
\begin{align*}
x^{\prime }&=-x+a y \\
y^{\prime }&=-x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| 6409 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| 6410 |
\begin{align*}
\left (x^{2}-2 x -3\right ) y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
\end{align*}
Series expansion around \(x=4\). |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 6411 |
\begin{align*}
x \left (x +1\right ) y^{\prime \prime }-4 y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.802 |
|
| 6412 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{2}+x_{3} \\
x_{2}^{\prime }&=-2 x_{1}-x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 6413 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 6414 |
\begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=4 t \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 6415 |
\begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| 6416 |
\begin{align*}
\left (1-x \right ) x^{2} y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 6417 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 6418 |
\begin{align*}
\left (4 x^{4}+2 x^{2}+1\right ) y+4 x^{3} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.803 |
|
| 6419 |
\begin{align*}
\left (\tan \left (x \right )^{2}-1\right ) y^{\prime \prime }-4 \tan \left (x \right )^{3} y^{\prime }+2 y \sec \left (x \right )^{4}&=\left (\tan \left (x \right )^{2}-1\right ) \left (1-2 \sin \left (x \right )^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.803 |
|
| 6420 |
\begin{align*}
y^{\prime \prime }&=y+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 6421 |
\begin{align*}
3 t^{2}-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 6422 |
\begin{align*}
x^{\prime \prime }+x&=\cos \left (\frac {9 t}{10}\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 6423 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=8 \,{\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 6424 |
\begin{align*}
3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| 6425 |
\begin{align*}
y^{\prime \prime }+x^{4} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.804 |
|
| 6426 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| 6427 |
\begin{align*}
16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| 6428 |
\begin{align*}
4 y^{\prime \prime }+20 y^{\prime }+25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| 6429 |
\begin{align*}
5 x^{5} y^{\prime \prime \prime \prime }+4 x^{4} y^{\prime \prime \prime }+x^{2} y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| 6430 |
\begin{align*}
y^{\prime \prime }+2 n^{2} y^{\prime }+n^{4} y&=\sin \left (k x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 6431 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-2 x}+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 6432 |
\begin{align*}
x^{\prime }&=12 x+18 y \\
y^{\prime }&=-8 x-12 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 6433 |
\begin{align*}
y^{\prime }&=\left (x^{2}-1\right ) \left (x^{3}-3 x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 6434 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 6435 |
\begin{align*}
v^{\prime \prime }+\frac {2 v^{\prime }}{r}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 6436 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 6437 |
\begin{align*}
\left (3 x^{2}+8 x +4\right ) y^{\prime \prime }+\left (16+12 x \right ) y^{\prime }+6 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 6438 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right )+2 x^{2}+5 x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 6439 |
\begin{align*}
y^{\prime \prime }-{\mathrm e}^{x} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 6440 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x} \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 6441 |
\begin{align*}
x \left (-1+{y^{\prime }}^{2}\right )&=2 y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 6442 |
\begin{align*}
x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.806 |
|
| 6443 |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }-4 x&=2 t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 6444 |
\begin{align*}
x^{\prime \prime }+x&=\cos \left (\frac {7 t}{10}\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 6445 |
\begin{align*}
x^{2} y^{\prime \prime }&=\left (3 x -2 y^{\prime }\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 6446 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 6447 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 6448 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{-2 t} \\
x_{2}^{\prime }&=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 6449 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2}-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 6450 |
\begin{align*}
x_{1}^{\prime }&=-\frac {x_{1}}{2}-\frac {x_{2}}{8}+\frac {{\mathrm e}^{-\frac {t}{2}}}{2} \\
x_{2}^{\prime }&=2 x_{1}-\frac {x_{2}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 6451 |
\begin{align*}
2 t^{2} y^{\prime \prime }-y^{\prime } t +\left (1+t \right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 6452 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-3 x_{2} \\
x_{3}^{\prime }&=x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 6453 |
\begin{align*}
2 y_{1}^{\prime }+y_{2}^{\prime }-4 y_{1}-y_{2}&={\mathrm e}^{x} \\
y_{1}^{\prime }+3 y_{1}+y_{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 6454 |
\begin{align*}
y^{\prime }&={\mathrm e}^{3 x}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 6455 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=x +{\mathrm e}^{x m} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 6456 |
\begin{align*}
x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=4 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 6457 |
\begin{align*}
9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 6458 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 6459 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\left (x^{2}+x \right ) {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 6460 |
\begin{align*}
x^{\prime }&=7 x+6 y \\
y^{\prime }&=2 x+6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 6461 |
\begin{align*}
x^{\prime \prime }+9 x&=10 \cos \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 6462 |
\begin{align*}
x^{2} y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+5 \,{\mathrm e}^{2 x} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.809 |
|
| 6463 |
\begin{align*}
2 y \left (x \,{\mathrm e}^{x^{2}}+\sin \left (x \right ) \cos \left (x \right ) y\right )+\left (2 \,{\mathrm e}^{x^{2}}+3 y \sin \left (x \right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.809 |
|
| 6464 |
\begin{align*}
x^{\prime }&=-4 x-y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 6465 |
\(\left [\begin {array}{cccc} 1 & 0 & 4 & 0 \\ 0 & 1 & 4 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 3 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.809 |
|
| 6466 |
\begin{align*}
x^{\prime \prime }+x^{\prime }-2 x&=3 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 6467 |
\begin{align*}
y^{\prime \prime }+y&=2 \cos \left (x \right )+2 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 6468 |
\begin{align*}
y^{\prime \prime }-4 y&=2 \sin \left (\frac {x}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 6469 |
\begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 6470 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 6471 |
\begin{align*}
y^{\prime \prime }-i y^{\prime }+12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 6472 |
\begin{align*}
y^{\prime \prime }-\left (1+\frac {3}{2 x}\right ) y^{\prime }+\frac {3 y}{2 x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 6473 |
\begin{align*}
2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 6474 |
\begin{align*}
4 x^{2} y^{\prime \prime }+3 y^{\prime } x +y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 6475 |
\begin{align*}
x^{\prime }-2 x+y&=0 \\
x+y^{\prime }-2 y&=-5 \,{\mathrm e}^{t} \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 6476 |
\begin{align*}
y^{\prime }+4 \csc \left (x \right )&=\left (3-\cot \left (x \right )\right ) y+\sin \left (x \right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.810 |
|
| 6477 |
\begin{align*}
-2 y+y^{\prime } x +x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.810 |
|
| 6478 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{x}+6 x -5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 6479 |
\begin{align*}
y^{2}+\cos \left (x \right )+\left (2 y x +\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.810 |
|
| 6480 |
\begin{align*}
y_{1}^{\prime }&=y_{2}-y_{3} \\
y_{2}^{\prime }&=y_{1}+y_{3}-{\mathrm e}^{-t} \\
y_{3}^{\prime }&=y_{1}+y_{2}+{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 2 \\
y_{3} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 6481 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 6482 |
\begin{align*}
-2 y+y^{\prime \prime }&=4 x^{2} {\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| 6483 |
\begin{align*}
i^{\prime \prime }-4 i^{\prime }+2 i&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| 6484 |
\begin{align*}
4 t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 6485 |
\begin{align*}
\sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t}&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.812 |
|
| 6486 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 6487 |
\begin{align*}
y^{\prime } x&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 6488 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 6489 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 6490 |
\begin{align*}
x^{\prime }&=4 x+3 y-6 \,{\mathrm e}^{3 t} \\
y^{\prime }&=x+6 y+2 \,{\mathrm e}^{3 t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 6491 |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }+16 y&=4 \\
y \left (0\right ) &= {\frac {5}{4}} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 6492 |
\begin{align*}
y^{\prime \prime }+9 y&=\sin \left (3 t \right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 6493 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\frac {{\mathrm e}^{-x}}{\sin \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 6494 |
\begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=3 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 6495 |
\begin{align*}
x^{\prime }&=4 x-y \\
y^{\prime }&=x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 6496 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 6497 |
\begin{align*}
\left (x^{2}-2 x -3\right ) y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
\end{align*}
Series expansion around \(x=-4\). |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 6498 |
\begin{align*}
y^{\prime }+y^{2}&=x^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.813 |
|
| 6499 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+25 y&=64 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 6500 |
\begin{align*}
{\mathrm e}^{y}+x \,{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|