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Answer check: differential initial value problem

  • Thread starter bakin
  • Start date
  • #1
58
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Homework Statement


solve the IVP

y''-8y'+16y=0

y(0)=2
y'(0)=7


Homework Equations





The Attempt at a Solution



auxiliary equation:
r2-8r+16=0
(r-4)2=0
so we have r=4 with m=2

y(x)= c1e4x+c2xe4x

y(0)--> c1e0 + 0 = 2
c1=2
now we have:
y(x)=2e4x+c2xe4x

take first derivative
y'(x) = 8e4x+c2e4x+4c2xe4x (product rule)

y'(0) ----> 8e0+c2e0+ 0 = 7
8+c2=7
c2=-1

so our final equation is:

y(x)=2e4x-xe4x

Everything seems ok, but just wanted to run it by here to make sure it's all done correctly. thanks all!
 

Answers and Replies

  • #2
142
0
Looks fine to me
 
  • #3
33,173
4,858
It's much easier to check that a potential solution actually works than it is to get the solution. For your problem all you need to do are the following:
  1. Verify that y(x) = 2e4x + xe4x satisfies y'' - 8y' + 16y = 0.
  2. Verify that y(0) = 2.
  3. Verify that y'(0) = 7.

If your solution satisfies the differential equation and initial conditions, you can bask in the warm glow of confidence that you nailed that problem.
 
  • #4
58
0
......I didn't even think of trying that. Thanks guys!
 

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