Is anyone able to do this?

Im having lots of problems

Results 1 to 5 of 5

- Jul 11th 2011, 11:21 AM #1

- Joined
- Nov 2010
- Posts
- 5

- Jul 11th 2011, 01:53 PM #2

- Jul 11th 2011, 02:17 PM #3

- Joined
- Feb 2008
- Posts
- 410

## Re: ODE Problem

There's probably an easier way to do this, but one valid and straightforward method is to convert to the system

$\displaystyle \left[\begin{array}{c}x_1\\x_2\end{array}\right]'=\left[\begin{array}{cc}0&1\\-400&0\end{array}\right]\left[\begin{array}{c}x_1\\x_2\end{array}\right]$,

where $\displaystyle i(t)=x_1$. We use this to find the fundamental matrix

$\displaystyle X(t)=\left[\begin{array}{cc}-\cos 20t&(\sin 20t)/20\\20i\cos 20t&i\sin 20t\end{array}\right]$

and determine $\displaystyle i(t)=a(-\cos 20t)+b(\sin 20t)/20$ for some constants $\displaystyle a,b\in\mathbb{R}$. It's easy to verify that the solution to the IVP in (i) is then given by $\displaystyle i(t)=5\cos 20t$.

- Jul 11th 2011, 02:24 PM #4

- Joined
- Nov 2010
- Posts
- 5

## Re: ODE Problem

Hi. Thanks for the reply

I should have been more specific sorry. its part ii) that Im really stuck with. sorry

for part i) I put the values into the quadratic formula and then with the obtained values substituted them into general solution giving me the desired graph that i was looking for

If you could help me with part ii) that would be great.

thanks

- Jul 11th 2011, 09:35 PM #5