# Undetermined Coefficients, more than one term on RHS

1. Mar 15, 2010

### Linday12

1. The problem statement, all variables and given/known data
y''-49y=7cos(7x)+7+e^(7x)

3. 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.

2. Mar 15, 2010

### rock.freak667

You just add the yp]'s for the individual functions.

yp=Aex+Bcosx+Csinx.

3. Mar 15, 2010

### Linday12

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

4. Mar 15, 2010

### anubis01

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

5. Mar 15, 2010

### rock.freak667

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.