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linear equations

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r(n) means "r subscript n"

The function y=e^(rx) has two values, r(1) and r(2) that satisfy the equation
2y''+y'-y=0.

How can I show that every number of the family of functions

y=a*e^[r(1)x] + b*e^[r(2)x]

is also a solution to the equation 2y''+y'-y=0?

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https://brainmass.com/math/linear-algebra/every-number-family-functions-416011

Solution Summary

This solution exemplifies linear equations.

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