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6. Find the solution of the initial value problem y" -y2y = cos z, y(0) = 0, y'(0)=-1

6. Find the solution of the initial value problem y" -y2y = cos z, y(0) = 0, y'(0)=-1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6. Find the solution of the initial value problem y" -y-2y = cos z, y(0) = 0, y'(0) = -1
Transcribed Image Text:6. Find the solution of the initial value problem y" -y-2y = cos z, y(0) = 0, y'(0) = -1
Expert Solution
Step 1

The given initial value problem is ,

      y''-y'-2y = cosx   ;   y(0)=0 , y'(0)=-1

Then the general solution is given by ,

          y(x) =  yc+ yp

where  yc is a complementary function and yp is a particular solution .

(.)   1f(D2)cos(ax) =  1f-a2cos(ax)   ;  f(-a2)≠0

(.)  If  m1  ,  m2 are two real and distinct  roots of a quadratic auxiliary equation , then 

         yc =  c1em1x+ c2em2x

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