| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12401 |
\begin{align*}
x^{\prime \prime }-2 x^{\prime }&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| 12402 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} \ln \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| 12403 |
\begin{align*}
x^{\prime }&=x+2 y+t -1 \\
y^{\prime }&=3 x+2 y-5 t -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| 12404 |
\begin{align*}
y^{\prime }&=-5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| 12405 |
\begin{align*}
2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.844 |
|
| 12406 |
\begin{align*}
-2 y^{\prime }+y^{\prime \prime } x&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.844 |
|
| 12407 |
\begin{align*}
x \left (-x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| 12408 |
\begin{align*}
\left (x +1\right ) y^{\prime \prime }-x^{2} y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| 12409 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=4 \sin \left (3 x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| 12410 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=2 \,{\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| 12411 |
\begin{align*}
t^{2} y^{\prime \prime }+2 y^{\prime } t -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| 12412 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| 12413 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| 12414 |
\begin{align*}
\left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.845 |
|
| 12415 |
\begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| 12416 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| 12417 |
\begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y&={\mathrm e}^{x} \left (\left (7+8 x \right ) \cos \left (2 x \right )+\left (8-4 x \right ) \sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| 12418 |
\begin{align*}
t^{2} y^{\prime \prime }-y^{\prime } t +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| 12419 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| 12420 |
\begin{align*}
\left (x -y\right ) y^{\prime }+x {y^{\prime }}^{2}+x \left (x +y\right ) y^{\prime \prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.846 |
|
| 12421 |
\begin{align*}
\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.846 |
|
| 12422 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=\sec \left (2 t \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| 12423 |
\begin{align*}
x_{1}^{\prime }&=3 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*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 5 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| 12424 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.847 |
|
| 12425 |
\begin{align*}
y y^{\prime \prime } \sin \left (x \right )+\left (\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y\right ) y^{\prime }&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.847 |
|
| 12426 |
\begin{align*}
y^{\prime }&=\frac {1}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.847 |
|
| 12427 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=-x_{1} \\
x_{3}^{\prime }&=-x_{4} \\
x_{4}^{\prime }&=x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| 12428 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 t}}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| 12429 |
\begin{align*}
t y^{\prime \prime }-y^{\prime }&=3 t^{2}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| 12430 |
\begin{align*}
y^{\prime }-a \left (t \right ) y&=\delta \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| 12431 |
\(\left [\begin {array}{cccc} 5 & 1 & 0 & 9 \\ 0 & 1 & 0 & 9 \\ 0 & 0 & 0 & 9 \\ 0 & 0 & 0 & 0 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.848 |
|
| 12432 |
\begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u&=3 \cos \left (\frac {t}{4}\right ) \\
u \left (0\right ) &= 2 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| 12433 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| 12434 |
\begin{align*}
y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.849 |
|
| 12435 |
\begin{align*}
y^{\prime \prime } x +v y^{\prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.849 |
|
| 12436 |
\begin{align*}
2 y^{\prime } \left (1+y^{\prime }\right )+\left (x -y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.849 |
|
| 12437 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+x&=5 \sin \left (2 t \right )+{\mathrm e}^{t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| 12438 |
\begin{align*}
x^{\prime }&=-2 x+3 y \\
y^{\prime }&=3 x-2 y \\
z^{\prime }&=-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| 12439 |
\begin{align*}
x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y&=x^{4}+2 x -5 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.849 |
|
| 12440 |
\begin{align*}
x^{\prime }+5 x+y&={\mathrm e}^{t} \\
y^{\prime }-x+3 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| 12441 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\
y \left (1\right ) &= {\mathrm e} \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| 12442 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=\delta \left (t -3\right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| 12443 |
\begin{align*}
x_{1}^{\prime }&=7 x_{1}-x_{2}+2 \,{\mathrm e}^{6 t} \\
x_{2}^{\prime }&=x_{1}+5 x_{2}+6 t \,{\mathrm e}^{6 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| 12444 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| 12445 |
\begin{align*}
4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| 12446 |
\begin{align*}
b y+2 x^{2} \left (a +x \right ) y^{\prime }+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.850 |
|
| 12447 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&={\mathrm e}^{-3 t} \\
x \left (0\right ) &= {\frac {1}{2}} \\
x^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| 12448 |
\begin{align*}
y^{\prime \prime }-y&=\cos \left (x \right ) \cosh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| 12449 |
\begin{align*}
x x^{\prime \prime }-{x^{\prime }}^{2}+{\mathrm e}^{t} x^{2}&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.850 |
|
| 12450 |
\begin{align*}
t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| 12451 |
\begin{align*}
y&=y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.851 |
|
| 12452 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| 12453 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-2 x_{3} \\
x_{3}^{\prime }&=3 x_{1}+2 x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| 12454 |
\begin{align*}
t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| 12455 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| 12456 |
\(\left [\begin {array}{ccc} 1 & 0 & 0 \\ -6 & 8 & 2 \\ 12 & -15 & -3 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.852 |
|
| 12457 |
\begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| 12458 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| 12459 |
\begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| 12460 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| 12461 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| 12462 |
\begin{align*}
y^{\prime \prime } x +x {y^{\prime }}^{2}-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| 12463 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +\left (-x^{2}+9\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| 12464 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1} \\
y_{2}^{\prime }&=3 y_{1}-2 y_{2} \\
y_{3}^{\prime }&=2 y_{2}+3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| 12465 |
\begin{align*}
y^{\prime }&=-3 y+z-w \\
z^{\prime }&=5 y-z-7 w \\
w^{\prime }&=-y+z-3 w \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| 12466 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+6 \,{\mathrm e}^{3 t} \\
x_{2}^{\prime }&=x_{1}+x_{2}+4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| 12467 |
\begin{align*}
9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.853 |
|
| 12468 |
\begin{align*}
x^{\prime }&=8 x+2 y-17 \\
y^{\prime }&=4 x+y-13 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.853 |
|
| 12469 |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.853 |
|
| 12470 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=2 x^{2} {\mathrm e}^{-2 x}+3 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.853 |
|
| 12471 |
\begin{align*}
3 {y^{\prime }}^{5}-y y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.853 |
|
| 12472 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{-x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.853 |
|
| 12473 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.853 |
|
| 12474 |
\begin{align*}
x^{\prime }&=-10 x+y+7 z \\
y^{\prime }&=-9 x+4 y+5 z \\
z^{\prime }&=-17 x+y+12 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 6 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.853 |
|
| 12475 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.853 |
|
| 12476 |
\begin{align*}
t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.854 |
|
| 12477 |
\begin{align*}
y^{\prime \prime }+9 y&=\csc \left (x \right ) \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.854 |
|
| 12478 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 y^{\prime } x +2 y&=x^{2}+3 x -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.854 |
|
| 12479 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.854 |
|
| 12480 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=3 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.854 |
|
| 12481 |
\begin{align*}
y_{1}^{\prime }&=4 y_{1}-y_{2}-4 y_{3} \\
y_{2}^{\prime }&=4 y_{1}-3 y_{2}-2 y_{3} \\
y_{3}^{\prime }&=y_{1}-y_{2}-y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.855 |
|
| 12482 |
\begin{align*}
\left (-x^{2}+x \right ) y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.855 |
|
| 12483 |
\begin{align*}
y^{\prime \prime }&=x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.855 |
|
| 12484 |
\begin{align*}
y+\left (-x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.855 |
|
| 12485 |
\begin{align*}
x^{\prime }&=-x-y \\
y^{\prime }&=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\
z^{\prime }&=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.855 |
|
| 12486 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y&=4 x -8 \\
y \left (1\right ) &= 4 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.855 |
|
| 12487 |
\(\left [\begin {array}{ccc} 2 & -4 & 0 \\ -4 & 0 & 0 \\ 0 & 0 & 0 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.855 |
|
| 12488 |
\(\left [\begin {array}{ccc} -1 & 0 & 3-i \\ 0 & 1 & 0 \\ 3+i & 0 & 0 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.855 |
|
| 12489 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.856 |
|
| 12490 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.856 |
|
| 12491 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+3 y^{\prime } x +a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.856 |
|
| 12492 |
\begin{align*}
x^{\prime }&=y+\tan \left (t \right )^{2}-1 \\
y^{\prime }&=\tan \left (t \right )-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.856 |
|
| 12493 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.857 |
|
| 12494 |
\begin{align*}
9 x^{2} y^{\prime \prime }+9 y^{\prime } x -\left (1+3 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.857 |
|
| 12495 |
\begin{align*}
2 y^{3} y^{\prime }+x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.857 |
|
| 12496 |
\(\left [\begin {array}{ccc} 5 & 0 & 0 \\ 4 & -4 & -2 \\ -2 & 12 & 6 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.857 |
|
| 12497 |
\begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-4 y \\
z^{\prime }&=-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.857 |
|
| 12498 |
\begin{align*}
y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.857 |
|
| 12499 |
\begin{align*}
y^{\prime }&=5 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.857 |
|
| 12500 |
\begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.858 |
|