Undetermined Coefficients, more than one term on RHS

[Linday12]

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.

 

[rock.freak667]

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

For example, if your RHS was e^x+cosx, your y_p would be
y_p=Ae^x+Bcosx+Csinx.

 

[Linday12]

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

 

[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^(\lambdax)
using sum rule yp=Acos(wx)+Bsin(wx)+C+De^(\lambdax)

edit: guess rock beat me to it

 

[rock.freak667]

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

Just be sure to note that you will have to modify your y_p a bit, since '7' appears as a root in your auxiliary equation.