Find a linear homogeneous constant-coefficient equation with the given general

hroncits8y

hroncits8y

Answered question

2021-12-03

With the given general solution, locate a linear homogeneous constant-coefficient equation.
y(x)=(A+Bx+Cx2)e2x

Answer & Explanation

Charles Wee

Charles Wee

Beginner2021-12-04Added 14 answers

By looking at the general solution, we must locate the roots of the characteristic equation.
providing a general answer:
y=(A+Bx+Cx2)e2x
This means that r1=r2=r3=2, so characteristic equation is:
(r2)3=r36r2+12r8=0
Corresponding differential equation is:
y(3)6y +12y8y=0
Result:
y(3)6y +12y8y=0

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