Consider the initial value problem y" – 5y' – 4y = sin(t) y(0) = 5, y'(0) = 2 A. Use the Laplace transform to transform it into an algebraic equation. B. Solve the algebraic equation for the laplace transform of the solution: L{y} = Y(s). (Do not try to solve for y(t) and do not even simplify the expression for Y(s).)

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A: We will find out the required solution.

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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.