Question: (a)(4 points) Find the Laplace transform off(t)=0tv3e-(t-v)sin(t-v)dv.(b)(3 points) Solve the integral equationy(t)-t=0te-2vy(t-v)dv(c)(4 points) Use Laplace transforms to solve the integro-differential equationy'=t+0tvy(t-v)dv,y(0)=0

(a)(4 points) Find the Laplace transform off(t)=0tv3e-(t-v)sin(t-v)dv.(b)(3 points) Solve the integral equationy(t)-t=0te-2vy(t-v)dv(c)(4 points) Use Laplace transforms to solve the integro-differential equationy'=t+0tvy(t-v)dv,y(0)=0

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