Question: 5. In this problem we will solve a differential equation by making a convenient change of variable. Consider the following differential equation By thy' -

5. In this problem we will solve a differential equation by making a convenient change of variable. Consider the following differential equation By" thy' - y -0. We will assume t > 0. (a) (3 points) Define t -t(r) - et, considering r a new variable. Verify that dy - y'lez )er da2 - y" (etje?* + y'(ez )ez. (b) (4 points) By substituting in the differential equation, show that in the variable r the equation becomes do? - y - 0. (c) (4 points) Find the fundamental set of equations of the previous equation. (d) (4 points) Using the previous part and replacing t - er, find the fundamental solutions of the original differential equation

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