Find the General Solution: y" +y' - 6y = 2x

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter5: Polynomial And Rational Functions
Section: Chapter Questions
Problem 27PT: Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and...
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Find the General Solution:
y" + y' - 6y = 2x
Transcribed Image Text:Find the General Solution: y" + y' - 6y = 2x
Expert Solution
Step 1

The given equation is a second order linear differential equation having constant coefficients.

The general solution of given equation has to be found as the sum of general solution yg of its corresponding homogenous equation and a particular integral solution yp of its inhomogeneous equation.

First of all, we have to formulate and solve the characteristic equation

λ2 +λ - 6 = 0

λ1 = 2 , λ2 = -3

Hence, yg = Aeλ1x + Beλ2x

Therefore, yg = Ae2x + Be-3x

 

 

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