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JefeNorte

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## Homework Statement

Given the differential equation for y=y(x)

(1) L[y]=y"+2by'+yb^2=(e^(-bx))/(x^2) x>0

a)find the complementary solution of (1) by solving L[y]=0

b)Solve (1) by introducing the transformation y(x)=(e^(-bx))*v(x) into (1) and obtaining and solving completely a differential equation for v(x). Use this to identify the particular solution

## The Attempt at a Solution

Follwing the steps outline at http://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx

I converted y"+by'+yb^2 to r^2+2br+b^2=0

By factoring I determined that r1=r2=-b

so the complimentary solution should be y=c1*e^(-bt)+c2*e^(-bt)

Is this the right way to solve for a complimentary solution? If so how do I "induce the transformation to solve fro the particular solution?"