Hi can you help me to do that probem?(see image) =x + 3x are, respectively,(a) Verify that yp = 3e* and y,particular solutions ofy" – 6y' + 5y = -9e2xandУ — бу' + 5у %3D 5x? + 3х — 16.(b) Use part (a) to find particular solutions ofу" — бу' + 5у %3D 5x2 + 3х — 16 — 9е2гand y" – 6y' + 5y = – 10x² – 6x + 32 + e2*.

To verify the given statement and to find particular solutions by using the given statement.

Answered: (a) Verify that yp, = 3e2* and y,, =x²…

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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(a) Verify that yp, = 3e2* and y,, =x² + 3x are, respectively, particular solutions of y" – 6y' + 5y = -9e2* and У — бу' + 5у %3D 5x? + 3х — 16. (b) Use part (a) to find particular solutions of y" - 6y' + 5y = 5x² + 3x – 16 – 9e2x and y" – 6y' + 5y = –10x² – 6x + 32 + e²x.