Answered: find the general solution by finding…

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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Related questions

Question

find the general solution by finding the homogeneous solution and a particular solution.

1) y" + 4y' = x

and the correct answer is y = c1 + c2e^(-4x) + 1/8(x^2) - 1/16. can you please show me how to get to the correct answer?

so we can seek a solution of the form yp = =Ax + B

Expert Solution

Step 1: Introduction

Given information:

The differential equation: $y apostrophe apostrophe plus 4 y apostrophe equals x$

To find:

The general solution by finding the homogeneous solution and a particular solution.

Concept used:

We will solve this second-order linear differential equation by first finding the homogeneous solution and then adding a particular solution. The homogeneous solution solves the equation without the non-homogeneous term (in this case, the
$x$ on the right-hand side), and the particular solution deals with the non-homogeneous term.