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Using Reduction of Order to find a Second Solution

Given that y1(x)=e^-x is a solution of y'' + 2y' + y =0, find second solution using the method of reduction of order.

I substituted y =ve^-x so y' = v'e^-x - v^-x; y''= v''e^-x -v'e^-x +v e^-x

I came out of that with v''e^-x + v'e^-x =0 I think the next step is to seperate variables. Looking for help to finish the problem.

Solution Summary

Reduction of order is used to find a second solution to a differential equation. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.