The function f(t) satisfies the differential equation d2f/dt2 + f = 0 and the auxiliary conditions, f(0) = 0, df/dt (0) = 4. The Laplace transform of f (t) is given by

Question

Christina · Accepted Answer

apply the laplace transform of derivatives
(d2f/dt2)+f =0
then apply all the given conditions
after applying laplace transform of derivatives it will come as 
1. s (square)*L(f(t))-s*4+L(f(t))=0
2. (s(square)+1)+L(f(t))=4
you will find the answer then :)

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The function f(t) satisfies the differential equation d2f/dt2 + f = 0 and the auxiliary conditions, f(0) = 0, df/dt (0) = 4. The Laplace transform of f (t) is given by

Answer is "4/(s2 + 1)"

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