Question 2 The function y(t) satisfies the initial value problem dạy dy +5 dt? +6y(t)= 0, y(0) = 0, y' (O)=5. dt (a) 5 S

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Question 2 The function y(t) satisfies the initial value problem dạy dy +5 dt? +6y(t)= 0, y(0) = 0, y' (O)=5. dt (a) 5 Show that Y(s) = where Y(S)=L(y(t)} (5+3)(s+2) (b) By expressing Y(s) in terms of its partial fractions show that 5 5 Y(s) S+3 5+2 + (c) By finding the inverse of y(s), determine the y(t).