| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 7501 |
\begin{align*}
y^{\prime \prime }+4 y&=2 t -8 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 7502 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 7503 |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 7504 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}-9 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7505 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=4 \sqrt {x}\, {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.559 |
|
| 7506 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+y&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7507 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7508 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7509 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7510 |
\begin{align*}
x^{\prime \prime }+42 x^{\prime }+x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7511 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+6 y&=10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7512 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7513 |
\begin{align*}
y^{\prime }&=\left (-2+y\right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7514 |
\begin{align*}
y^{\prime \prime }+3 x^{2} y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7515 |
\begin{align*}
{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7516 |
\begin{align*}
y^{\prime }-y&=x^{2} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7517 |
\begin{align*}
y^{\prime \prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7518 |
\begin{align*}
{y^{\prime }}^{2}-x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7519 |
\begin{align*}
-y+x y^{\prime }+x^{3} y^{\prime \prime \prime }&=x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7520 |
\begin{align*}
y^{\prime }&=\frac {x -1}{x +1} \\
y \left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7521 |
\begin{align*}
y^{\prime \prime }-10 y^{\prime }+25 y&=6 \,{\mathrm e}^{-5 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7522 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}-16} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7523 |
\begin{align*}
y^{\prime \prime }+y&=8 \,{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7524 |
\begin{align*}
x^{\prime }&=-\frac {3 x}{2}+y \\
y^{\prime }&=-\frac {x}{4}-\frac {y}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7525 |
\begin{align*}
x^{\prime }&=2 x+\frac {3 y}{2} \\
y^{\prime }&=-\frac {3 x}{2}-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7526 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7527 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7528 |
\begin{align*}
\left (x -1\right ) \left (x +2\right ) y^{\prime \prime }+\left (x +\frac {1}{2}\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7529 |
\begin{align*}
y^{\prime }&=t^{2}+1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7530 |
\begin{align*}
y^{\prime \prime }+25 y&=\cos \left (5 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 7531 |
\begin{align*}
36 y^{\prime }+36 y^{2}-12 y+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 7532 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 x} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 7533 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 7534 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2} \\
x_{2}^{\prime }&=16 x_{1}-5 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 7535 |
\begin{align*}
y+\left (x -2 x^{2} y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.560 |
|
| 7536 |
\(\left [\begin {array}{cccc} 1 & 0 & 4 & 0 \\ 0 & 1 & 4 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 3 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.560 |
|
| 7537 |
\begin{align*}
x^{\prime \prime }+9 x&=\sin \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 7538 |
\begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 7539 |
\begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.560 |
|
| 7540 |
\begin{align*}
x^{\prime }&=3 x-4 y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 7541 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 7542 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 7543 |
\begin{align*}
2 y-x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| 7544 |
\begin{align*}
y^{\prime \prime }-x y^{\prime \prime \prime }+{y^{\prime \prime \prime }}^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.560 |
|
| 7545 |
\begin{align*}
\left (2 x +1\right ) y^{\prime \prime }-\left (1-2 x \right ) y^{\prime }-\left (3-2 x \right ) y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -2 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| 7546 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| 7547 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\cos \left ({\mathrm e}^{-x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| 7548 |
\begin{align*}
y^{\prime \prime }&=\frac {\left (1+3 x \right ) y^{\prime }}{\left (x -1\right ) \left (x +1\right )}-\frac {36 \left (x +1\right )^{2} y}{\left (x -1\right )^{2} \left (5+3 x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.561 |
|
| 7549 |
\begin{align*}
-y^{\prime }+{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.561 |
|
| 7550 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| 7551 |
\begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| 7552 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| 7553 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| 7554 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=-3 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| 7555 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}-y_{2} \\
y_{2}^{\prime }&=3 y_{1}-2 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| 7556 |
\begin{align*}
x^{2}+x y^{\prime }&=3 x +y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| 7557 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (\cos \left (2 x \right )+\sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| 7558 |
\(\left [\begin {array}{ccc} 1 & -2 & 0 \\ 0 & 0 & 0 \\ -5 & 0 & 7 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.561 |
|
| 7559 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+10 y&=20-{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 7560 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-24 y&=16-\left (x +2\right ) {\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 7561 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&=-256 t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 7562 |
\begin{align*}
y^{\prime }&=2 \sin \left (x \right ) \cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 7563 |
\begin{align*}
x^{\prime }&=3 t^{2}+4 t \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 7564 |
\begin{align*}
{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.562 |
|
| 7565 |
\begin{align*}
y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x}&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.562 |
|
| 7566 |
\begin{align*}
3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 7567 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime }&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✗ |
✗ |
0.562 |
|
| 7568 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 7569 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 7570 |
\begin{align*}
\left (x y^{\prime }+y\right )^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| 7571 |
\begin{align*}
\left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7572 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+{\mathrm e}^{t} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7573 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7574 |
\begin{align*}
w^{\prime }+w x&={\mathrm e}^{x} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7575 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x^{2}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7576 |
\begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7577 |
\begin{align*}
y^{\prime \prime }+\left (1+4 i\right ) y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7578 |
\begin{align*}
2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7579 |
\begin{align*}
y^{\prime \prime }&=\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {\left (a \,x^{4}+10 x^{2}+1\right ) y}{4 x^{6}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.563 |
|
| 7580 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=18 x^{2}+3 x +4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7581 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7582 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.563 |
|
| 7583 |
\begin{align*}
v^{\prime \prime }-6 v^{\prime }+13 v&={\mathrm e}^{-2 u} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7584 |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }&=\lambda y^{\prime \prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.563 |
|
| 7585 |
\begin{align*}
x^{\prime }&=a y \\
y^{\prime }&=-a x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7586 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7587 |
\begin{align*}
y^{\prime \prime }+4 y&=t \sin \left (t \right ) \\
y \left (0\right ) &= {\frac {7}{9}} \\
y^{\prime }\left (0\right ) &= -{\frac {5}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7588 |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=5 \cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7589 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right )-2 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7590 |
\begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| 7591 |
\begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 7592 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 7593 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 7594 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-t}-4 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 7595 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}-3 x_{2}-2 x_{3} \\
x_{2}^{\prime }&=8 x_{1}-5 x_{2}-4 x_{3} \\
x_{3}^{\prime }&=-4 x_{1}+3 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 7596 |
\begin{align*}
4 y+y^{\prime \prime }&=3 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 7597 |
\begin{align*}
y^{\prime \prime }-y&=x^{2} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 7598 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=-5 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 7599 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| 7600 |
\begin{align*}
y&=x y^{\prime }+k {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|