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Find impulse response of the following equation,d2y(t)dt2+5dy(t)dt+6y(t)=x(t)
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Solution:

d2y(t)dt2+5dy(t)dt+6y(t)=x(t)

Applying Laplace transform of the given equation,

S2Y(S)+5SY(S)+6Y(S)=X(S)Y(S)(S2+5S+6)=X(S)

 Transfer function H(S)=Y(S)X(S)=1(S2+5S+6)

H(S)=Y(S)=1S2+5S+6

H(S)=1(S+3)(S+2)=AS+3+BS+21=A(S+2)+B(S+3)

H(S)=1S+3+1S+2

Applying Inverse Laplace transform,

h(t)=e3tu(t)+e2tu(t)

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