Find: (a) Use Partial Fractions Decomposition to write the rational function as the sum of simpler...

  

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Find: (a) Use Partial Fractions Decomposition to write the rational function as the sum of simpler expressions (b) Obtain the time-domain solution, x(t), by finding the inverse Laplace Transform of X(S) (c) Consider the inverse question, if the ODE (X + ax + bx = f(t)) had initial conditions, x(0) = 0 and *(0) = 1, what was the input function in the time domain, f(t) X(s) s² +15 = (s² + 5s + 6) (s² +9) Find: (a) Use Partial Fractions Decomposition to write the rational function as the sum of simpler expressions (b) Obtain the time-domain solution, x(t), by finding the inverse Laplace Transform of X(S) (c) Consider the inverse question, if the ODE (X + ax + bx = f(t)) had initial conditions, x(0) = 0 and *(0) = 1, what was the input function in the time domain, f(t) X(s) s² +15 = (s² + 5s + 6) (s² +9)