# Undetermined Coefficients, more than one term on RHS

## Homework Statement

y''-49y=7cos(7x)+7+e^(7x)

## The Attempt at a Solution

I have no idea how to solve this Differential equation. I could solve one that has y''-49y=one term, but I'm stumped with more than one.

First, I get the homogeneous equation, y''-49y=0 and fine y_c, then use the formulas to get y_p, but that is where I'm stumped, since I'm not sure how to find it with the 3 terms on the R.H.S.

## Answers and Replies

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rock.freak667
Homework Helper
You just add the yp]'s for the individual functions.

For example, if your RHS was ex+cosx, your yp would be
yp=Aex+Bcosx+Csinx.

Awesome. That sounds like exactly what I needed to know. Thanks!

for more than one term on the right hand side you just sum up the result. i.e for 7cos(7x)
yp=Acos(wx)+Bsin(wx). for 7 yp=C and for e^(7x) yp=De^($$\lambda$$x)
using sum rule yp=Acos(wx)+Bsin(wx)+C+De^($$\lambda$$x)

edit: guess rock beat me to it

rock.freak667
Homework Helper
Awesome. That sounds like exactly what I needed to know. Thanks!
Just be sure to note that you will have to modify your yp a bit, since '7' appears as a root in your auxiliary equation.