What is the trial particular solution for this differential equation?

[dan5]

Homework Statement

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

y_p(x) = R(h) cos (ht - ∅(h))

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

Homework Equations

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

The Attempt at a Solution

solving the equation as a quadratic in coefficients on sin and cos, hbar = 12

 

[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?

 

[dan5]

yes y_p is the particular solution.

Well i thought of using a trial particular solution of

y_p= 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)