If y=xe^7 is a solution of a linear homogeneous 2nd order DE, then another solution might be

capellitad9 2022-07-17 Answered
If y = x e 7 x is a solution of a linear homogeneous 2nd order DE, then another solution might be?
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Answers (1)

Damarion Pierce
Answered 2022-07-18 Author has 11 answers
For a second order linear homogenous equations,
If roots of auxiliary equation are
1. real and distinct then the solution is
y = C 1 e m 1 x + C 2 e m 2 x
2.real and equal then the solution is
y = C 1 e m x + C 2 x e m x
3.complex then the solution is
y = e α x ( C 1 cos ( β x ) + C 2 sin ( β x ) )
Given y = x e 7 x is the solution
the solution is similar for the case of real and equal roots
therefor the other solution is
y = e 7 x
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