Question

Entered Answer Preview (5-2+25)(s +10) (+25)s+2%-6) At least one of the answers above is NOT correct. (1 point) Consider the following initial value problem: Using Y for the Laplace transform of y(f), le..Y = L {y()). find the equation you get by taking the Laplace transform of the differential equation and solve for To find a solution to the IVP above, what steps must next be performed next? A. Take the derivative of Y(s). B. Plug in the given values to Y(s). C. Apply the Laplace transform to Y(s). O D. Apply the inverse Laplace transform to Y(s) (using partial fraction decomposition where necessary).

Answer 1

"Given y"" - 4y' - 12y = sin(st) (1) y(0) = -1, y'(0) = 6 taking L. T on both sides of (1) we get L{y""} - 4 L {y'} - 12 L{y} = L{sin 5t} or [s^2 L{y} - s y(0) - y(0)] - 4[s L[y}- y(0)] - 12 L{y} = 5/s^2 + 25 [therefore L{sin at} = a/s62 + a^2] or, (s^2 - 4s - 12) y(s) = -s + 10 + 5/s^2 + 25 [therefore y(0) = -1, y'(0) = 6] or, (s^2 - 4s - 12) y(s) = (s^2 + 25) (10 - s) + 5/(s^2 + 25) or, y(s) = 25 s - 25 s + 10 s^2 - s^3/(s^2 + 25) (s + 2) (s - 6) [therefore s^2 - 4s - 12 = (s + 2) (s - 6) option - D "