Use the Laplace transform to solve the given initial-value problem.
y′ + 2y = sin 4t, y(0) = 1
the Laplace transform for the first derivative:
then for IVP:
Answer: y(t)=−0.2cos(4t)+0.1sin(4t)+1.2e−2ty(t)=-0.2 cos(4t)+0.1 sin(4t)+1.2 e^{-2t}y(t)=−0.2cos(4t)+0.1sin(4t)+1.2e−2t
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