# Linear dependence of solutions

One solution to ty"-(t+2)y'+2y=0 is exp(t)

Find a second linearly independent solution.

https://brainmass.com/math/linear-algebra/linear-dependence-solutions-28803

#### 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:

So:

This ...

#### Solution Summary

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

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