Finding and solving llinear equations


Question:

Llinear equations

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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Mathematics: Finding and solving llinear equations
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