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.

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A: A detailed solution is given below.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.