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12. у" — 2у — Зу %3D 0, у(4) 3 -3, у' (4) 3D — 17 - 17

12. у" — 2у — Зу %3D 0, у(4) 3 -3, у' (4) 3D — 17 - 17

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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Solve the shifted data IVPs by the Laplace transform. Show
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12. у" — 2у — Зу %3D 0, у(4) 3 -3, у' (4) 3D — 17 - 17
Transcribed Image Text:12. у" — 2у — Зу %3D 0, у(4) 3 -3, у' (4) 3D — 17 - 17
Expert Solution
Step 1

Since the method of Laplace transform can be used only if the initial condition are given at 0.

The given differential equation is y''t-2y't-3y=0 with y4=-3, y'4=-17.

Let x=t-4 and ux=yx+4. Differentiating it with respect to x:

                       dudx=dydt×dtdxu'x=y't

Again differentiating it with respect to x:

                       d2udx2=ddty't×dtdxu''x=y''t

Putting these value into given differential equation becomes:

                 y''t-2y't-3y=0u''x-2u'x-3ux=0

With initial condition u0=y0+4=-3 and u'0=y'0+4=-17.

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