| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12401 |
\begin{align*}
y^{\prime \prime } x&=y^{\prime } \left (2-3 y^{\prime } x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.037 |
|
| 12402 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\
y^{\prime }\left (1\right ) &= 0 \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.037 |
|
| 12403 |
\begin{align*}
x^{\prime }&=3 x-2 y+24 \sin \left (t \right ) \\
y^{\prime }&=9 x-3 y+12 \cos \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.037 |
|
| 12404 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{i \omega t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.037 |
|
| 12405 |
\begin{align*}
y^{\prime }+a y-b \sin \left (c x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.038 |
|
| 12406 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x +\left (3 x -2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.038 |
|
| 12407 |
\begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{2 t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.038 |
|
| 12408 |
\begin{align*}
x^{\prime \prime }-x^{\prime }&=6+{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.039 |
|
| 12409 |
\begin{align*}
y^{\left (6\right )}+2 y^{\left (5\right )}+5 y^{\prime \prime \prime \prime }&=x^{3}+x^{2} {\mathrm e}^{-x}+{\mathrm e}^{-x} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.039 |
|
| 12410 |
\begin{align*}
-3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.039 |
|
| 12411 |
\begin{align*}
y_{1}^{\prime }&=5 y_{1}-2 y_{2} \\
y_{2}^{\prime }&=4 y_{1}-y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.039 |
|
| 12412 |
\begin{align*}
y^{\prime \prime \prime }&=x +\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.039 |
|
| 12413 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +p^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.040 |
|
| 12414 |
\begin{align*}
\left (-1+x \right ) y^{\prime \prime }+y^{\prime } x +\frac {y}{x}&=0 \\
\end{align*}
Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
2.040 |
|
| 12415 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{3 x} \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.040 |
|
| 12416 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.041 |
|
| 12417 |
\begin{align*}
y^{\prime \prime }+16 y&=5 \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.042 |
|
| 12418 |
\begin{align*}
t y^{\prime \prime }+y^{\prime } t +2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
2.043 |
|
| 12419 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime } x +2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.043 |
|
| 12420 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=x \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.043 |
|
| 12421 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+4 y&=x \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.044 |
|
| 12422 |
\begin{align*}
{y^{\prime }}^{2}+\left (y^{\prime }-y\right ) {\mathrm e}^{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.045 |
|
| 12423 |
\begin{align*}
y^{\prime \prime } x -\left (x +4\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.045 |
|
| 12424 |
\begin{align*}
x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.046 |
|
| 12425 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=8 x^{2} {\mathrm e}^{2 x} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.046 |
|
| 12426 |
\begin{align*}
x^{\prime \prime }+x&=\sin \left (2 t \right )-\cos \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.046 |
|
| 12427 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.046 |
|
| 12428 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.047 |
|
| 12429 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.047 |
|
| 12430 |
\begin{align*}
y^{\prime } x +x +\left (a x +2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.048 |
|
| 12431 |
\begin{align*}
2 \left (1-x \right ) x y^{\prime \prime }+y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.048 |
|
| 12432 |
\begin{align*}
y^{\prime \prime } x -\left (a x +1\right ) y^{\prime }-b \,x^{2} \left (b x +a \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.048 |
|
| 12433 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.048 |
|
| 12434 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.048 |
|
| 12435 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.048 |
|
| 12436 |
\begin{align*}
t^{2} y^{\prime \prime }+3 y^{\prime } t +\frac {5 y}{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.049 |
|
| 12437 |
\begin{align*}
y^{\prime }&=2 y \\
y \left (\ln \left (3\right )\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.049 |
|
| 12438 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.049 |
|
| 12439 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.049 |
|
| 12440 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.049 |
|
| 12441 |
\begin{align*}
y^{\prime \prime }-9 y&=20 \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 18 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.049 |
|
| 12442 |
\begin{align*}
x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +3 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.050 |
|
| 12443 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.051 |
|
| 12444 |
\begin{align*}
\left (3 x^{2}+1\right ) y^{\prime \prime }+13 y^{\prime } x +7 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.051 |
|
| 12445 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{x}+\left (1-x \right ) \left ({\mathrm e}^{2 x}-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.052 |
|
| 12446 |
\begin{align*}
y^{\prime }&=2 \,{\mathrm e}^{2 t}-4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.052 |
|
| 12447 |
\begin{align*}
\left (1+t \right ) y+y^{\prime } t&=t \\
y \left (\ln \left (2\right )\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.053 |
|
| 12448 |
\begin{align*}
y+y^{\prime }&=\frac {1}{t^{2}+1} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.053 |
|
| 12449 |
\begin{align*}
\left (y^{\prime } x +a \right )^{2}-2 a y+x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.053 |
|
| 12450 |
\begin{align*}
-y+y^{\prime }&={\mathrm e}^{4 t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.053 |
|
| 12451 |
\begin{align*}
4 x^{\prime \prime }+9 x&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.055 |
|
| 12452 |
\begin{align*}
c y^{\prime }+\left (b x +a \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.056 |
|
| 12453 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }-7 x^{3} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.056 |
|
| 12454 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-3\right ) y&={\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.056 |
|
| 12455 |
\begin{align*}
y^{\prime \prime }+2 a \,x^{n} y^{\prime }+a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.056 |
|
| 12456 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-4 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.056 |
|
| 12457 |
\begin{align*}
y^{\prime \prime }+n^{2} y&={\mathrm e}^{x} x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.056 |
|
| 12458 |
\begin{align*}
x^{\prime }&=2 x-3 y+t \,{\mathrm e}^{-t} \\
y^{\prime }&=2 x-3 y+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.056 |
|
| 12459 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=24 \cosh \left (t \right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.056 |
|
| 12460 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=\cos \left (t \right )+57 \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.056 |
|
| 12461 |
\begin{align*}
y^{\prime }&=\sqrt {x -y} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.057 |
|
| 12462 |
\begin{align*}
y^{\prime } x&=a \,x^{m}-b y-c \,x^{n} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.057 |
|
| 12463 |
\begin{align*}
-2 b y+2 a y^{\prime }+x \left (b x +a \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.057 |
|
| 12464 |
\begin{align*}
x \left (x +1\right )^{2} y y^{\prime \prime }-x \left (x +1\right )^{2} {y^{\prime }}^{2}+2 \left (x +1\right )^{2} y y^{\prime }-a \left (2+x \right ) y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.057 |
|
| 12465 |
\begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.058 |
|
| 12466 |
\begin{align*}
y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.058 |
|
| 12467 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.058 |
|
| 12468 |
\begin{align*}
4 y^{\prime \prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| 12469 |
\begin{align*}
y^{2} \left (1-{y^{\prime }}^{2}\right )&=b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| 12470 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| 12471 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-15 y&=16 t \,{\mathrm e}^{-t}-15 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -9 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| 12472 |
\begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=3 \,{\mathrm e}^{-2 t}-6 \,{\mathrm e}^{-5 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| 12473 |
\begin{align*}
y^{\prime \prime \prime \prime }-\lambda ^{4} y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\pi \right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| 12474 |
\begin{align*}
{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.060 |
|
| 12475 |
\begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }+11 y^{\prime } x +9 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.060 |
|
| 12476 |
\begin{align*}
y+\left (2 t -y \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.060 |
|
| 12477 |
\begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.060 |
|
| 12478 |
\begin{align*}
\left (x^{2}-25\right ) y^{\prime \prime }+2 y^{\prime } x +y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
2.062 |
|
| 12479 |
\begin{align*}
y^{\prime \prime }+x^{3} y^{\prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.062 |
|
| 12480 |
\begin{align*}
y^{\prime }&=\frac {-x +F \left (x^{2}+y^{2}\right )}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.062 |
|
| 12481 |
\begin{align*}
8 x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (-1+x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.062 |
|
| 12482 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.062 |
|
| 12483 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.062 |
|
| 12484 |
\begin{align*}
t^{2} y^{\prime \prime }+5 y^{\prime } t -2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| 12485 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\alpha \left (\alpha +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| 12486 |
\begin{align*}
x^{\prime }&=x+2 y+z \\
y^{\prime }&=6 x-y \\
z^{\prime }&=-x-2 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| 12487 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| 12488 |
\begin{align*}
y^{\prime \prime }+7 y^{\prime }+6 y&=250 \,{\mathrm e}^{t} \cos \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -7 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| 12489 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| 12490 |
\begin{align*}
x^{\prime }&=t +2 \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| 12491 |
\begin{align*}
x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.064 |
|
| 12492 |
\begin{align*}
a y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.064 |
|
| 12493 |
\begin{align*}
y^{\prime } x +y-x \sin \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.064 |
|
| 12494 |
\begin{align*}
5 x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.064 |
|
| 12495 |
\begin{align*}
y^{\prime \prime }+w^{2} y&=g \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.064 |
|
| 12496 |
\begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.064 |
|
| 12497 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{x}+x \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.065 |
|
| 12498 |
\begin{align*}
y^{\prime }+\frac {26 y}{5}&=\frac {97 \sin \left (2 t \right )}{5} \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.065 |
|
| 12499 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&={\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.065 |
|
| 12500 |
\begin{align*}
4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.065 |
|