HOMEWORK 1 Due September 15 1. Find the Laplace Transform of the following: a. f(t)=(sint +4-1)...

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HOMEWORK 1 Due September 15 1. Find the Laplace Transform of the following: a. f(t)=(sint +4²-1) b. f(t)-r¹ sinwr 2. Find the Inverse Laplace Transforms of the following: 1 a. F(s)=- s(s+25+2) b. F(s)- C. F(3) - 5(5+2) 3² (5+1)(5+3) 3. Solve the following differential equations using Laplace Transforms a. -3+2y=2e" withy(0)-2 and (0)=-1 -12y+32y=32u(t) with zero initial b. conditions +3dy(t) + 2y(t) = 0 dt c. d²y(t) dt² with initial conditions y(0) = a and y(¹)(0) = dy(t) dt -It=o=b HOMEWORK 1 Due September 15 1. Find the Laplace Transform of the following: a. f(t)=(sint +4²-1) b. f(t)-r¹ sinwr 2. Find the Inverse Laplace Transforms of the following: 1 a. F(s)=- s(s+25+2) b. F(s)- C. F(3) - 5(5+2) 3² (5+1)(5+3) 3. Solve the following differential equations using Laplace Transforms a. -3+2y=2e" withy(0)-2 and (0)=-1 -12y+32y=32u(t) with zero initial b. conditions +3dy(t) + 2y(t) = 0 dt c. d²y(t) dt² with initial conditions y(0) = a and y(¹)(0) = dy(t) dt -It=o=b