engineering mathematics

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QUESTION 3 Solve for x only by using D-operator methods in the following set of simultaneous equations: (D)x(D+1)y=2etx+(D1)y=e3t QUESTION 4 4.1L{t4e2t} (3) 4.2L{etcosht} 4.3L1{s2+4s+20s+2} 4.4L1{s297s27} [13] QUESTION 5 Determine the unique solution of the following differential equations by using Laplace transforms: 5.1 y(x)+6y(x)+13y(x)=0, if y(0)=3 and y(0)=7. (9) 5.2y(t)+2y(t)3y(t)=e3t, if y(0)=0 and y(0)=0. (10) [18]