# A system of 1st order diffy q's

## 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

Nothing, really.

## The Attempt at a Solution

x1=u , x2=u' => x2' = -.25x2 -4x1 + 2cos(3t); x1'=x2

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

I know x1 and x2 are functions of t, so the second equation is saying that the derivative of x1 is x2, and x1'(0)=x2(0)=-2; x1(0)=1. Where do I go from here?

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Dick
Homework Helper

## 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

Nothing, really.

## The Attempt at a Solution

x1=u , x2=u' => x2' = -.25x2 -4x1 + 2cos(3t); x1'=x2

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

I know x1 and x2 are functions of t, so the second equation is saying that the derivative of x1 is x2, and x1'(0)=x2(0)=-2; x1(0)=1. Where do I go from here?
You don't go anywhere from there. The problem asked to change the u(t) equation into a coupled initial value problem for two first order equations. I think you did that with your x1(t) and x2(t).

You don't go anywhere from there. The problem asked to change the u(t) equation into a coupled initial value problem for two first order equations. I think you did that with your x1(t) and x2(t).
I didn't read the problem! Hahaha!

Mark44
Mentor
I didn't read the problem! Hahaha!
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