Find the Laplace transforms of the followingfunctions: \int_{0}^{t} \cos \left(\frac{1}{2} \tau\right) \sin (2 t-\tau) d \tau g(t)=e^{4-2 t} \text { 滕 } e^{9 t} \sin (t) Find the inverse Laplace transforms of thefollowing functions: F(s)=\frac{3}{4 s^{5}+4 s^{3}} G(s)=\frac{11}{5 s^{3}+5 s} Given the IVP: y" +81y = cos(21), y(0) = 0, y' (0) = 12. A) Use the Laplace transform to find y(s). B) Find the solution of the above IVP.

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