Explore BrainMass
Share

# Linearly independent solutions

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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.

© BrainMass Inc. brainmass.com October 9, 2019, 10:37 pm ad1c9bdddf
https://brainmass.com/math/ordinary-differential-equations/linearly-independent-solutions-226616

#### Solution Preview

The solution of the Posting is in the attached file.

Thanks for using BrainMass.com. Have a great day.

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.

...

#### Solution Summary

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

\$2.19