- #1

accountkiller

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## Homework Statement

You are given a solution - find the homogeneous, 2nd order differential equation ay'' + by' + cy = 0

## Homework Equations

y(x) = c

_{1}+ c

_{2}e

^{-10x}

## The Attempt at a Solution

I found the derivatives first.

y'(x) = c

_{1}- 10c

_{2}e

^{-10x}

y''(x) = c

_{1}+ 100c

_{2}e

^{-10x}

But I have no idea where to go from there. The answer is y'' + 10y' = 0. Looking at that answer, yes I see why that is the answer, but what work did I have to show to get to that answer?

I'd appreciate any guidance, thanks!

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