I dont know if I solved it correctly so far and I was wondering what I need to do to get the natural system response
$$y''+3y'-4y=x$$
2026-03-27 14:58:27.1774623507
I need help with this LTI system-differential equation
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$$y''+3y'-4y=x$$ $$Y(s)(s^2+3s-4)=X(s)$$ For the Transfert Function, we have: $$H(s)= \dfrac {Y(s)}{X(s)}=\dfrac 1 {s^2+3s-4}$$ $$H(s)=\dfrac 1 {(s-1)(s+4)}$$ $$5H(s)=\dfrac 1 {(s-1)}-\dfrac 1 {(s+4)}$$ For the impulse response, we have: $$h(t)=\dfrac 1 5 \left (e^{t}-e^{-4t}\right)$$ You added an extra $s$ at the numerator. Apart from this, you applied the method correctly.