Problem 1. Use Laplace transform, partial-fraction expansion and inverse Laplace transform to solve the following differential...

     

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Problem 1. Use Laplace transform, partial-fraction expansion and inverse Laplace transform to solve the following differential equations. 2y(t) + y(t)=e; y(0)=0 ÿ(t)+2y(t) + y(t)=1; y(0) = y(0) = 0 (1) (2) Problem 2. Find the inverse Laplace transforms of the following functions by expanding the fractional part of X(s) into partial fractions. a. X(s): = 1 s(S+1) (s+3)(s+10) (s+15) Problem 1. Use Laplace transform, partial-fraction expansion and inverse Laplace transform to solve the following differential equations. 2y(t) + y(t)=e; y(0)=0 ÿ(t)+2y(t) + y(t)=1; y(0) = y(0) = 0 (1) (2) Problem 2. Find the inverse Laplace transforms of the following functions by expanding the fractional part of X(s) into partial fractions. a. X(s): = 1 s(S+1) (s+3)(s+10) (s+15)