The initial value problem y" + 5y" - 8y' - 12y = -48, y(0) = 8, y'(0) = 29, y"(0) = -83 is given. If the Laplace transform of y(t) is Y(S), first find Y(s). Then using Y(s) find the solution of the given initial value problem. 8s3 + 69s2 - 25 - 48 s4 + 5s3 - 8s2 - 12s A. Y(s) = y(t) = e - 3e t + 6e - 4 8s3 + 69s2 - 25 - 48 s4+ 5s3 - 8s2 - 12s B. Y(s) = y(t) = e - 3e6+ 6e + 4 8s3 + 69s2 - 2s + 48 C. Y(s) = , y(t) = et - 3e6L + 6e + 4 s4 + 553 - 8s2 - 12s 8s3 + 69s2 - 2s + 48 s4 + 5s3 - 8s2 - 12s D. Y(s) = , y(t) = e - 3e 6 + 6e - 4

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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.