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Undetermined Coefficients, more than one term on RHS

  • Thread starter Linday12
  • Start date
  • #1
54
0

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

  • #2
rock.freak667
Homework Helper
6,230
31
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.
 
  • #3
54
0
Awesome. That sounds like exactly what I needed to know. Thanks!
 
  • #4
149
1
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^([tex]\lambda[/tex]x)
using sum rule yp=Acos(wx)+Bsin(wx)+C+De^([tex]\lambda[/tex]x)

edit: guess rock beat me to it
 
  • #5
rock.freak667
Homework Helper
6,230
31
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.
 

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