An FE Exam Math Problem in Ordinary Differential Equations

“The Fundamentals of Engineering (FE) exam is generally the first step in the process of becoming a professional licensed engineer (P.E.). It is designed for recent graduates and students who are close to finishing an undergraduate engineering degree from an EAC/ABET-accredited program” – FE Exam NCEES

For most engineering majors, mathematics is a required part of the examination. Here is a question from ordinary differential equations.

ode solution

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Repeated roots in ordinary differential equation – next independent solution – where does that come from?

When solving a fixed-constant linear ordinary differential equation where the characteristic equation has repeated roots, why do we get the next independent solution in the form of x^n*e^(m*x)?  Show this through an example.

See this pdf file for the answer.

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