Consider the Second Order Linear Differential Equation ty'' − (t + 1)y' + y = 0, t > 0. A. Show that y1(t) = e^t is a solution of this equation. B. Use the Method of Reduction of Order to find a...

Consider the Second Order Linear Differential Equation

ty'' − (t + 1)y' + y = 0, t > 0.

A. Show that y1(t) = e^t is a solution of this equation.

B. Use the Method of Reduction of Order to find a second independent solution y = y2 of the given equation.

Hint — Recall that the Method of Reduction of Order uses the assumption that a second independent solution y = y2 is of the form y = v(t) y1(t).