Consider the following initial value problem z" +52=0, 2(0)-6, z'(0)-5. (a) Using X for the Laplace transform of a(t), that is, X(a)=(x(t)), find the equation obtains by taking the Laplace transform of the above differential equation. 2X-5s-5+6(sX-5) / -0 help (formulas) (6) Solve the algebraic equation from part (a) for X(a)- (e) Write the expression for X(a) from part (b) in its partial fraction decomposition. X(0) X(0) A s+a + 4+ B s+b' help (formulas) where a b help (formulas) Finally, by finding the inverse Laplace transform of X(a), solve the original intial value problem. In other words, determine 2(1)(X(0)} help (formulas)

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