6.2 Transforms of derivatives and ODEs: Problem 1 (20 points) Consider the following initial value problem: x" -5x-24x=sin(2t), x(0) = 1, x'(0) = = −4. Using X for the Laplace transform of x(t), i.e., X = L{x(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for X(s) = ☐ help (formulas) Book: Section 6.2 of Notes on Diffy Qs

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Q: g(0)=sin 0:

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A: Applying “ln” on both sides of equation and simplifying.