If we have a linear system with the following differential equation:
d2y/dt2+7*dy/dt+12*y=dx/dt+5*x
So H(s) = (s+5)/((s+4)*(s+3)) = -1/(s+4)+2/(s+3)--> h(t) = (-e^(-4*t)+2*e^(-3*t))*u(t)
(Please calculate the unit impulse response by Laplace transform and verify the result by yourself)
Why this answer does not satisfy the differential equation?
The right answer is:
h(t) = (-2*e^(-4*t)+3*e^(-3*t))*u(t)
d2y/dt2+7*dy/dt+12*y=dx/dt+5*x
So H(s) = (s+5)/((s+4)*(s+3)) = -1/(s+4)+2/(s+3)--> h(t) = (-e^(-4*t)+2*e^(-3*t))*u(t)
(Please calculate the unit impulse response by Laplace transform and verify the result by yourself)
Why this answer does not satisfy the differential equation?
The right answer is:
h(t) = (-2*e^(-4*t)+3*e^(-3*t))*u(t)