# Homework Help: Differential equation

1. Feb 4, 2012

### dan5

1. The problem statement, all variables and given/known data

y'' + 24y' +432y = cos (wt)

yp(x) = R(h) cos (ht - ∅(h))

find R(h)
and hbar = value for h which R(h) is max.
and ∅(hbar)

2. Relevant equations

double angle formula for cos
cos (a-b) = cos a cos b + sin a sin b

3. The attempt at a solution

solving the equation as a quadratic in coefficients on sin and cos, hbar = 12
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 4, 2012

### HallsofIvy

Frankly, I can't figure out what your question is. What is yp? Is it supposed to be a particular solution? If so, you will need to find yp' and yp'' and put them into the equation. What do you get when you do that?

3. Feb 4, 2012

### dan5

yes yp is the particular solution.

Well i thought of using a trial particular solution of

yp= A sin (Ht) + B cos (Ht)

which leaves me with

-AH2-24BH+432A = 0 for coefficients of sin(Ht)

and

-BH2+24AH+432B = 1 for coefficients of cos(Ht)

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