| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 9601 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+y&=3 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.299 |
|
| 9602 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.299 |
|
| 9603 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=3 \cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.299 |
|
| 9604 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=0 \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= -9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.299 |
|
| 9605 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.299 |
|
| 9606 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=9 x^{2}-12 x +2 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.299 |
|
| 9607 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.299 |
|
| 9608 |
\begin{align*}
y&=y^{\prime } x +1+4 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.299 |
|
| 9609 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&={\mathrm e}^{2 x} \left (x +3\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.299 |
|
| 9610 |
\begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.300 |
|
| 9611 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=5 \sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.300 |
|
| 9612 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.300 |
|
| 9613 |
\begin{align*}
2 y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.300 |
|
| 9614 |
\begin{align*}
y^{\prime \prime }-8 y^{\prime }+15 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.300 |
|
| 9615 |
\begin{align*}
y^{\prime }+\frac {2 y}{2 x -1}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.300 |
|
| 9616 |
\begin{align*}
4 t^{2} y^{\prime \prime }+4 y^{\prime } t +\left (16 t^{2}-1\right ) y&=16 t^{{3}/{2}} \\
y \left (\pi \right ) &= 0 \\
y^{\prime }\left (2 \pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.300 |
|
| 9617 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.300 |
|
| 9618 |
\begin{align*}
\left (-x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.301 |
|
| 9619 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&=-\cos \left (5 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.301 |
|
| 9620 |
\begin{align*}
y^{\prime } x&=\sin \left (x \right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.301 |
|
| 9621 |
\begin{align*}
x^{\prime }+x&={\mathrm e}^{t} \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.301 |
|
| 9622 |
\begin{align*}
y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.302 |
|
| 9623 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.302 |
|
| 9624 |
\begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.302 |
|
| 9625 |
\begin{align*}
10 x_{1}^{\prime }&=-x_{1}+x_{3} \\
10 x_{2}^{\prime }&=x_{1}-x_{2} \\
10 x_{3}^{\prime }&=x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.303 |
|
| 9626 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}-2 x_{3}+x_{4} \\
x_{2}^{\prime }&=3 x_{2}-5 x_{3}+3 x_{4} \\
x_{3}^{\prime }&=-13 x_{2}+22 x_{3}-12 x_{4} \\
x_{4}^{\prime }&=-27 x_{2}+45 x_{3}-25 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.303 |
|
| 9627 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.303 |
|
| 9628 |
\begin{align*}
x^{\prime \prime }-3 x&=\sin \left (y \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.303 |
|
| 9629 |
\begin{align*}
y^{\prime }-y&=x \sqrt {y} \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.304 |
|
| 9630 |
\begin{align*}
4 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.304 |
|
| 9631 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y&=x \left (x^{2}+x +1\right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.304 |
|
| 9632 |
\begin{align*}
x^{\prime }&=-5 x-2 y \\
y^{\prime }&=-x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.304 |
|
| 9633 |
\begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.304 |
|
| 9634 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y-z \\
z^{\prime }&=-y+2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.305 |
|
| 9635 |
\begin{align*}
x^{\prime \prime }-x&={\mathrm e}^{t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.305 |
|
| 9636 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{5}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.305 |
|
| 9637 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.305 |
|
| 9638 |
\begin{align*}
y^{3} \sin \left (2 x \right )-3 y^{2} \cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.305 |
|
| 9639 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.306 |
|
| 9640 |
\begin{align*}
y^{\prime \prime }+16 y&=16 \cos \left (4 x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.306 |
|
| 9641 |
\begin{align*}
y^{\prime }+4 y&={\mathrm e}^{-4 t} \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.306 |
|
| 9642 |
\begin{align*}
x^{\prime }&=-x+y-z \\
y^{\prime }&=2 x-y+2 z \\
z^{\prime }&=2 x+2 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.306 |
|
| 9643 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.306 |
|
| 9644 |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }-4 x&=3 \cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.306 |
|
| 9645 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }-8 y&={\mathrm e}^{x} \left (x^{2}+2\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.306 |
|
| 9646 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&={\mathrm e}^{2 x} \cos \left (x \right )+{\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.306 |
|
| 9647 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.307 |
|
| 9648 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.307 |
|
| 9649 |
\begin{align*}
8 x^{2} y^{\prime \prime }-2 x \left (-x^{2}-4 x +3\right ) y^{\prime }+\left (x^{2}+6 x +3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.308 |
|
| 9650 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=\sin \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.308 |
|
| 9651 |
\begin{align*}
y^{\prime \prime }-4 y&=12 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.309 |
|
| 9652 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.309 |
|
| 9653 |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{-x} \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.309 |
|
| 9654 |
\begin{align*}
x^{\prime }&=-6 x+2 y \\
y^{\prime }&=-3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.309 |
|
| 9655 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.309 |
|
| 9656 |
\begin{align*}
y^{\prime \prime }+y&=2 \sin \left (2 x \right ) \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.309 |
|
| 9657 |
\begin{align*}
y^{\prime \prime }+4 y&=3 \sec \left (2 t \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.309 |
|
| 9658 |
\begin{align*}
x^{\prime \prime }+9 x^{\prime }+8 x&=\sin \left (5 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.309 |
|
| 9659 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=50 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.310 |
|
| 9660 |
\begin{align*}
x^{2} y^{\prime \prime }-6 y&=\ln \left (x \right ) \\
y \left (1\right ) &= {\frac {1}{6}} \\
y^{\prime }\left (1\right ) &= -{\frac {1}{6}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.310 |
|
| 9661 |
\begin{align*}
x^{\prime }&=5 x+2 y+5 t \\
y^{\prime }&=3 x+4 y+17 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.310 |
|
| 9662 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.310 |
|
| 9663 |
\begin{align*}
x^{2}+y^{\prime } x&=3 x +y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.310 |
|
| 9664 |
\begin{align*}
y^{\prime \prime }+y&=8 x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.311 |
|
| 9665 |
\begin{align*}
y^{\prime \prime }+4 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.311 |
|
| 9666 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t} \operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.312 |
|
| 9667 |
\begin{align*}
-\left (5+4 x \right ) y+32 y^{\prime } x +16 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.312 |
|
| 9668 |
\begin{align*}
y y^{\prime \prime }&=-y \left (f^{\prime }\left (x \right )-y^{2} g^{\prime }\left (x \right )\right )+\left (f \left (x \right )+g \left (x \right ) y^{2}\right ) y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.312 |
|
| 9669 |
\begin{align*}
y^{\prime } x&=x y^{2}+a y+b \,x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.312 |
|
| 9670 |
\begin{align*}
{y^{\prime }}^{3}-{\mathrm e}^{2 x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.312 |
|
| 9671 |
\begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.313 |
|
| 9672 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
y^{\prime }\left (1\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.313 |
|
| 9673 |
\begin{align*}
x^{\prime }&=7 x+y-1-6 \,{\mathrm e}^{t} \\
y^{\prime }&=-4 x+3 y+4 \,{\mathrm e}^{t}-3 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.313 |
|
| 9674 |
\begin{align*}
t y^{\prime \prime }+y^{\prime }+t y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.313 |
|
| 9675 |
\begin{align*}
4 {y^{\prime }}^{2}-9 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.313 |
|
| 9676 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.313 |
|
| 9677 |
\begin{align*}
x^{\prime }&=4 \,{\mathrm e}^{-t}-2 \\
x \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.313 |
|
| 9678 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{x} \sin \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.313 |
|
| 9679 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 4 \\
y^{\prime \prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.313 |
|
| 9680 |
\begin{align*}
y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.314 |
|
| 9681 |
\begin{align*}
4 {y^{\prime }}^{2}+2 x \,{\mathrm e}^{-2 y} y^{\prime }-{\mathrm e}^{-2 y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.315 |
|
| 9682 |
\begin{align*}
x^{3}-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.315 |
|
| 9683 |
\begin{align*}
y^{\prime \prime \prime \prime }-16 y&=x^{2} \sin \left (2 x \right )+x^{4} {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.315 |
|
| 9684 |
\begin{align*}
y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.315 |
|
| 9685 |
\begin{align*}
x_{1}^{\prime }&=\frac {3 x_{1}}{4}+\frac {29 x_{2}}{4}-\frac {11 x_{3}}{2} \\
x_{2}^{\prime }&=-\frac {3 x_{1}}{4}+\frac {3 x_{2}}{4}-\frac {5 x_{3}}{2} \\
x_{3}^{\prime }&=\frac {5 x_{1}}{4}+\frac {11 x_{2}}{4}-\frac {5 x_{3}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.315 |
|
| 9686 |
\begin{align*}
\left (x^{2}+x \right ) y^{\prime }+2 x +1+2 \cos \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.315 |
|
| 9687 |
\begin{align*}
x^{\prime \prime }-9 x^{\prime }-10 x&=\cos \left (4 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.315 |
|
| 9688 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{2}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.316 |
|
| 9689 |
\begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.316 |
|
| 9690 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+2 x_{2}-x_{4} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+2 x_{4} \\
x_{3}^{\prime }&=3 x_{3} \\
x_{4}^{\prime }&=-x_{1}+2 x_{2}+2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.316 |
|
| 9691 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.316 |
|
| 9692 |
\begin{align*}
4 x^{2} y^{\prime \prime }+x \left (4 x^{2}+2 x +7\right ) y^{\prime }-\left (-7 x^{2}-4 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.317 |
|
| 9693 |
\begin{align*}
\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2}&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.317 |
|
| 9694 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.317 |
|
| 9695 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+40 y&=122 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.317 |
|
| 9696 |
\begin{align*}
x^{\prime \prime }-6 x^{\prime }-7 x&=4 z -7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.317 |
|
| 9697 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.317 |
|
| 9698 |
\begin{align*}
10 x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (66 x^{2}+13 x +13\right ) y^{\prime }-\left (10 x^{2}+4 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.318 |
|
| 9699 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-y&=t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.318 |
|
| 9700 |
\begin{align*}
y^{\prime } x +y&=\frac {1}{x^{3}} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.318 |
|