# Linearly independent solutions

Determine another linearly independent solution to y''+2xy'+2y=0 given that one homogeneous solution to this ODE is y_1(x)=exp(-x^2). Verify linear independence by calculating the wronskian.

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The solution of the Posting ID 226616

It is given that is one homogeneous solution of the equation

--------------------------(1)

Let be the complete solution of the equation (1), where is some function of to be determined.

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#### Solution Summary

This provides an example of finding a linearly independent solution to a differential equation.

$2.19