- #1

Jamin2112

- 986

- 12

## Homework Statement

Transform the given initial value problem into an initial value problem for the first two first order equations.

u'' + .25u' + 4u = 2cos(3t), u(0)=1, u'(0)=-2

## Homework Equations

Nothing, really.

## The Attempt at a Solution

x

_{1}=u , x

_{2}=u' => x

_{2}' = -.25x

_{2}-4x

_{1}+ 2cos(3t); x

_{1}'=x

_{2}

There's the system. I don't understand the initial value part, though; and my professor didn't do any examples.

I know x

_{1}and x

_{2}are functions of t, so the second equation is saying that the derivative of x

_{1}is x

_{2}, and x

_{1}'(0)=x

_{2}(0)=-2; x

_{1}(0)=1. Where do I go from here?