6. Following the directions below, use Laplace transforms to solve the following initial value problem. y" + y' – 12y = -218(t – 5), y(0) = = 0, y'(0) = 21 (a) Show that when one transforms the given initial value problem into an algebraic equation involving L{y} = Y(s), one obtains 21 -21 te-5s 3) Y(s) = (s + 4)(s – (s+4)(s – 3) (b) Use the expression for Y(s) given in part (a) to solve for y(t), the solution of the initial value problem.

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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.