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    Linear dependence of solutions

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    One solution to ty"-(t+2)y'+2y=0 is exp(t)
    Find a second linearly independent solution.

    © BrainMass Inc. brainmass.com March 4, 2021, 6:05 pm ad1c9bdddf


    Solution Preview

    Hi there!

    Here is the solution in two file formats as usual.
    I'm sorry it took me a while, but I wanted to show you two different methods how to approach this kind of problem (who know's in a test it might come handy).

    First Method: Wronskian

    Write the equation as:

    The two solutions must satisfy:

    Multiplying equation (2) by y1 and subtracting equation (1) multiplied by y2 we obtain:

    Using the Wronskian's definition:

    We see that:


    This ...

    Solution Summary

    The solution is 6 pages long and demonstrates two possible methods to solve the problem.