| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 5601 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 x+4 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| 5602 |
\begin{align*}
x^{\prime }+3 x-y&=0 \\
y^{\prime }+y-3 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| 5603 |
\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. |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| 5604 |
\begin{align*}
y^{\prime \prime }+y&=3 \delta \left (t -\pi \right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| 5605 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| 5606 |
\begin{align*}
x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (-3 x +4\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| 5607 |
\begin{align*}
\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| 5608 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-5 y&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| 5609 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| 5610 |
\begin{align*}
2 y^{\prime } \left (1+y^{\prime }\right )+\left (x -y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.445 |
|
| 5611 |
\begin{align*}
y \left (3-4 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| 5612 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-11 y^{\prime } x +16 y&=\frac {1}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| 5613 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| 5614 |
\begin{align*}
y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| 5615 |
\begin{align*}
4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| 5616 |
\begin{align*}
y^{\prime }+\frac {y}{x -1}&=0 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| 5617 |
\begin{align*}
y^{\prime \prime }-\sin \left (x \right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| 5618 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| 5619 |
\begin{align*}
y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| 5620 |
\begin{align*}
y^{\prime \prime }+y&=x^{2} \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi ^{2}}{4} \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 2 \pi \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| 5621 |
\begin{align*}
1+{\mathrm e}^{3 x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| 5622 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=-2 x_{1}-2 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=2 x_{1}+3 x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| 5623 |
\begin{align*}
y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.447 |
|
| 5624 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=-2 x_{1}+5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| 5625 |
\begin{align*}
y^{\prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| 5626 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| 5627 |
\begin{align*}
x^{\prime }&=5 x+3 y \\
y^{\prime }&=-6 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| 5628 |
\begin{align*}
y^{\prime \prime }+9 y&=\cos \left (3 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| 5629 |
\(\left [\begin {array}{ccc} -5 & -12 & 6 \\ 1 & 5 & -1 \\ -7 & -10 & 8 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.447 |
|
| 5630 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=\frac {x_{1}}{2}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| 5631 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +\left (2 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| 5632 |
\begin{align*}
x^{\prime }+x+2 y^{\prime }+3 y&=0 \\
x^{\prime }-2 x+5 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| 5633 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-5 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| 5634 |
\begin{align*}
x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (4 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| 5635 |
\begin{align*}
x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{\left (-x^{2}+1\right )^{2}}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.448 |
|
| 5636 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| 5637 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-3 x_{2} \\
x_{2}^{\prime }&=3 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| 5638 |
\begin{align*}
y y^{\prime }-2 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.448 |
|
| 5639 |
\begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=6 y_{1}+y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| 5640 |
\begin{align*}
y^{\prime } \left (y^{\prime } x -y+k \right )+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.448 |
|
| 5641 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.448 |
|
| 5642 |
\begin{align*}
y^{\prime \prime } x -x^{2} {y^{\prime }}^{2}+2 y^{\prime }+y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.448 |
|
| 5643 |
\(\left [\begin {array}{ccc} -2 & 6 & -18 \\ 12 & -23 & 66 \\ 5 & -10 & 29 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.448 |
|
| 5644 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y-z \\
z^{\prime }&=-y+2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| 5645 |
\begin{align*}
y \left (y-2 y^{\prime } x \right )^{2}&=2 y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| 5646 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=8 x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (1\right ) &= 2 \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| 5647 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| 5648 |
\begin{align*}
y^{\prime }&=y^{2} \left (y^{2}-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| 5649 |
\begin{align*}
y^{\prime \prime }&=g \left (x \right )+f \left (x \right ) y^{2}+\left (f \left (x \right )-2 y\right ) y^{\prime } \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.449 |
|
| 5650 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {15}{8}} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| 5651 |
\begin{align*}
\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.449 |
|
| 5652 |
\begin{align*}
x^{\prime }&=-\frac {9 x}{10}-2 y \\
y^{\prime }&=x+\frac {11 y}{10} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| 5653 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=\sec \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| 5654 |
\begin{align*}
x^{\prime }&=x-6 y \\
y^{\prime }&=-2 x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| 5655 |
\begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| 5656 |
\begin{align*}
y^{\prime \prime \prime }-y&=12 \sinh \left (t \right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= 7 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.449 |
|
| 5657 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-3 x_{2} \\
x_{2}^{\prime }&=6 x_{1}-7 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 8 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| 5658 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+6 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| 5659 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}+3 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}-x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| 5660 |
\begin{align*}
x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.450 |
|
| 5661 |
\begin{align*}
y^{2} {y^{\prime }}^{2}+y^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| 5662 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (1-3 x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| 5663 |
\begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| 5664 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| 5665 |
\begin{align*}
x^{2} y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+5 y \,{\mathrm e}^{2 x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.451 |
|
| 5666 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| 5667 |
\begin{align*}
y^{\prime }+20 y&=24 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| 5668 |
\begin{align*}
y^{\prime }&=y^{2}+2 y-3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| 5669 |
\begin{align*}
x^{\prime }&=-\lambda _{1} x \\
y^{\prime }&=\lambda _{1} x-\lambda _{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| 5670 |
\begin{align*}
y^{\prime \prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| 5671 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.451 |
|
| 5672 |
\begin{align*}
y^{\prime } x +y&=\sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.451 |
|
| 5673 |
\begin{align*}
x^{\prime }&=5 x-y \\
y^{\prime }&=3 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| 5674 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=13 t +17+40 \sin \left (t \right ) \\
y \left (0\right ) &= 30 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| 5675 |
\begin{align*}
y^{\prime }&=f \left (x \right ) f^{\prime }\left (x \right )+y f^{\prime }\left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 5676 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 5677 |
\begin{align*}
y^{\prime }&=\frac {2 x y^{2}+4 y \ln \left (2 x +1\right ) x +2 \ln \left (2 x +1\right )^{2} x +y^{2}-2+\ln \left (2 x +1\right )^{2}+2 y \ln \left (2 x +1\right )}{2 x +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 5678 |
\begin{align*}
4 x^{2} y^{\prime \prime }-x^{4} {y^{\prime }}^{2}+4 y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.452 |
|
| 5679 |
\begin{align*}
y+2 x y^{2}-x^{2} y^{3}+2 x^{2} y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 5680 |
\begin{align*}
x^{\prime }&=x-5 y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 5681 |
\begin{align*}
x^{\prime }&=z-y \\
y^{\prime }&=z-x \\
z^{\prime }&=z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 5682 |
\begin{align*}
4 y+4 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=\cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 5683 |
\begin{align*}
y^{\prime }&=x \sin \left (x^{2}\right ) \\
y \left (\frac {\sqrt {2}\, \sqrt {\pi }}{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 5684 |
\begin{align*}
y^{\prime } x&=x^{2}+2 x -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 5685 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=3 \delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 5686 |
\begin{align*}
-2 y+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 5687 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}-x_{2} \\
x_{2}^{\prime }&=3 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 5688 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=-5 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 5689 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 5690 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-2 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 5691 |
\begin{align*}
x_{1}^{\prime }&=-\frac {x_{1}}{10}+\frac {3 x_{2}}{40} \\
x_{2}^{\prime }&=\frac {x_{1}}{10}-\frac {x_{2}}{5} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -17 \\
x_{2} \left (0\right ) &= -21 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 5692 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y&=\left (x +1\right )^{3} {\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.454 |
|
| 5693 |
\begin{align*}
y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }&=-16 \,{\mathrm e}^{-2 x} \left (-x^{3}+x^{2}+x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 5694 |
\begin{align*}
x_{1}^{\prime }&=6 x_{1}-3 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 5695 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 5696 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=-4 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 5697 |
\begin{align*}
\left (-x^{2}+1\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +4 x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.454 |
|
| 5698 |
\begin{align*}
-y+y^{\prime }&=2 \cos \left (5 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 5699 |
\begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.454 |
|
| 5700 |
\begin{align*}
{y^{\prime }}^{2}+\left (x -2\right ) y^{\prime }-y+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|