| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 6501 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 6502 |
\begin{align*}
y_{1}^{\prime }&=3 y_{1}-2 y_{2} \\
y_{2}^{\prime }&=y_{2}-y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 6503 |
\begin{align*}
x^{\prime }&=3 x+y \\
y^{\prime }&=6 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 6504 |
\begin{align*}
x_{1}^{\prime }&=7 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| 6505 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| 6506 |
\begin{align*}
\left (-2 x^{3}+1\right ) y^{\prime \prime }-10 x^{2} y^{\prime }-8 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| 6507 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| 6508 |
\begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=\frac {x}{2}-\frac {3 y}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| 6509 |
\begin{align*}
x^{2} y^{\prime \prime }+4 y^{2}-6 y&=x^{4} {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.547 |
|
| 6510 |
\begin{align*}
x_{1}^{\prime }&=a x_{1}+5 x_{3} \\
x_{2}^{\prime }&=-x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| 6511 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+6 y x&=0 \\
\end{align*} Series expansion around \(x=4\). |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| 6512 |
\begin{align*}
t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| 6513 |
\begin{align*}
x_{1}^{\prime }&=-4 x_{2} \\
x_{2}^{\prime }&=4 x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| 6514 |
\begin{align*}
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| 6515 |
\begin{align*}
y^{\prime \prime \prime \prime }-6 y&=t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 9 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| 6516 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| 6517 |
\begin{align*}
x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| 6518 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| 6519 |
\begin{align*}
1+y^{\prime }&=2 y \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 6520 |
\begin{align*}
x_{1}^{\prime }&=2 x_{2} \\
x_{2}^{\prime }&=-2 x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 6521 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 6522 |
\begin{align*}
\left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-y x -2 y^{2}\right ) y^{\prime }-y \left (x -y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 6523 |
\begin{align*}
y^{\prime } t +y&=t \\
y \left (0\right ) &= 5 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✗ |
✓ |
0.549 |
|
| 6524 |
\begin{align*}
a x^{\prime }+b y^{\prime }&=\alpha x+\beta y \\
b x^{\prime }-a y^{\prime }&=\beta x-\alpha y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 6525 |
\begin{align*}
x^{\prime }&=-2 x+3 y \\
y^{\prime }&=-6 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 6526 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (-5 x +1\right ) y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 6527 |
\begin{align*}
y^{\prime }&=1+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 6528 |
\begin{align*}
y^{\prime \prime }-4 x^{2} y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 6529 |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2}+y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.549 |
|
| 6530 |
\begin{align*}
x^{\prime }&=4 x+a y \\
y^{\prime }&=8 x-6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 6531 |
\begin{align*}
c v^{\prime \prime }+\frac {v^{\prime }}{r}+\frac {v}{L}&=-\delta \left (t \right )+\delta \left (t -1\right ) \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 6532 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}-9 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 6533 |
\begin{align*}
x_{1}^{\prime }&=\frac {3 x_{1}}{4}-2 x_{2} \\
x_{2}^{\prime }&=x_{1}-\frac {5 x_{2}}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 6534 |
\begin{align*}
x_{1}^{\prime }&=4 x_{2} \\
x_{2}^{\prime }&=-4 x_{1} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 6535 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1} \\
x_{2}^{\prime }&=3 x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 6536 |
\begin{align*}
x^{\prime }&=-11 x-2 y \\
y^{\prime }&=13 x-9 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 6537 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +20 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 6538 |
\begin{align*}
a y y^{\prime \prime }&=\left (-1+a \right ) {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.552 |
|
| 6539 |
\begin{align*}
y^{\prime }&=\left (-1+y\right )^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.552 |
|
| 6540 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +\left (2+x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.552 |
|
| 6541 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 6542 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 6543 |
\begin{align*}
3 t^{2}-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 6544 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }&=1 \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 6545 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-6 y^{\prime } x -4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 6546 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 6547 |
\begin{align*}
y^{\prime \prime } x -2 y^{\prime }+y x&=0 \\
y \left (3\right ) &= 1 \\
y^{\prime }\left (3\right ) &= -2 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 6548 |
\begin{align*}
\left (-2 x^{2}+1\right ) y^{\prime \prime }+\left (2-6 x \right ) y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 6549 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 6550 |
\begin{align*}
a \left (-y+y^{\prime } x \right )^{2}+x^{2} y^{\prime \prime }&=b \,x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.553 |
|
| 6551 |
\begin{align*}
y^{\prime }&=y^{2}-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 6552 |
\begin{align*}
x^{\prime }&=10 x-5 y \\
y^{\prime }&=8 x-12 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 6553 |
\begin{align*}
y^{\prime }&=x^{2}+{\mathrm e}^{x}-\sin \left (x \right ) \\
y \left (2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 6554 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+1 \\
x_{2}^{\prime }&=x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 6555 |
\begin{align*}
x^{\prime }&=y+t \\
y^{\prime }&=x-t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 6556 |
\begin{align*}
y^{\prime }&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 6557 |
\begin{align*}
x^{\prime }-7 x+y&=0 \\
y^{\prime }-2 x-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 6558 |
\begin{align*}
\left (x -1\right )^{4} y^{\prime \prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 6559 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-3 x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| 6560 |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| 6561 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }&=1 \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| 6562 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| 6563 |
\begin{align*}
a \cos \left (y^{\prime }\right )+b y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.554 |
|
| 6564 |
\begin{align*}
x^{\prime }+y-t^{2}+6 t +1&=0 \\
-x+y^{\prime }&=-3 t^{2}+3 t +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| 6565 |
\begin{align*}
x^{\prime }-7 x+y&=0 \\
y^{\prime }-2 x-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| 6566 |
\begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }-6 y^{\prime }-12 y&=\sinh \left (x \right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.554 |
|
| 6567 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=2 t^{2}+4 \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| 6568 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| 6569 |
\begin{align*}
y^{\prime }&=t \sin \left (t^{2}\right ) \\
y \left (\sqrt {\pi }\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| 6570 |
\begin{align*}
y^{\prime }+z^{\prime }+6 y&=0 \\
z^{\prime }+5 y+z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| 6571 |
\begin{align*}
\frac {1}{x}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| 6572 |
\begin{align*}
3 x^{2} y^{\prime \prime }+2 y^{\prime } x +x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| 6573 |
\begin{align*}
u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5}&=\cos \left (t \right ) \\
u \left (0\right ) &= 2 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.556 |
|
| 6574 |
\begin{align*}
\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+8 x \right ) y^{\prime }+4 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| 6575 |
\begin{align*}
2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| 6576 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2} \\
x_{2}^{\prime }&=-x_{2} \\
x_{3}^{\prime }&=-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| 6577 |
\begin{align*}
y^{\prime \prime }&=a \left (-y+y^{\prime } x \right )^{k} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.556 |
|
| 6578 |
\begin{align*}
2 y^{\prime \prime \prime } y^{\prime }&=2 {y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.556 |
|
| 6579 |
\begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| 6580 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| 6581 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| 6582 |
\begin{align*}
y^{\prime \prime \prime }+y&={\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| 6583 |
\begin{align*}
x_{1}^{\prime }&=39 x_{1}+8 x_{2}-16 x_{3} \\
x_{2}^{\prime }&=-36 x_{1}-5 x_{2}+16 x_{3} \\
x_{3}^{\prime }&=72 x_{1}+16 x_{2}-29 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| 6584 |
\begin{align*}
x_{1}^{\prime }&=28 x_{1}+50 x_{2}+100 x_{3} \\
x_{2}^{\prime }&=15 x_{1}+33 x_{2}+60 x_{3} \\
x_{3}^{\prime }&=-15 x_{1}-30 x_{2}-57 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| 6585 |
\begin{align*}
t^{2} y^{\prime \prime }-t \left (1+t \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| 6586 |
\begin{align*}
3 y^{\prime }+12 y&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| 6587 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| 6588 |
\begin{align*}
t^{2} y^{\prime \prime }+t \left (1-2 t \right ) y^{\prime }+\left (t^{2}-t +1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| 6589 |
\begin{align*}
6 x^{2} y^{\prime \prime }+7 y^{\prime } x -\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 6590 |
\begin{align*}
\left (1-x \right ) x^{2} y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 6591 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= v \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 6592 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-y x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 6593 |
\begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (3 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 6594 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (t \right )+t \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 6595 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.558 |
|
| 6596 |
\begin{align*}
y^{\prime }&=x y^{3}+x^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.558 |
|
| 6597 |
\begin{align*}
x^{\prime }&=x+4 y \\
y^{\prime }&=-3 x+2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| 6598 |
\begin{align*}
x_{1}^{\prime }&=-40 x_{1}-12 x_{2}+54 x_{3} \\
x_{2}^{\prime }&=35 x_{1}+13 x_{2}-46 x_{3} \\
x_{3}^{\prime }&=-25 x_{1}-7 x_{2}+34 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 6599 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| 6600 |
\begin{align*}
\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y&=0 \\
\end{align*} Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.559 |
|