Question

What is the transfer function of dy(t)/dt = A*x(t) - B in the form of Y(s)/X(s) assuming zero initial conditions?

Answer 1

I'm not entirely sure, but I don't think this will give you a proper transfer function.

One thing you could do, though, is replace \(x(t)=u(t)+\dfrac{B}{A}\), so that the ODE becomes
\[\frac{\mathrm{d}}{\mathrm{d}t}y(t)=A\left(u(t)+\frac{B}{A}\right)-B=Au(t)\]then take the Laplace transform of both sides and solve for \(\dfrac{Y(s)}{U(s)}\), where \(U(s)=X(s)-\dfrac{B}{As}\). I'm not at all familiar with transfer functions, but from what I can see I just don't think there's a way of solving for \(\dfrac{Y(s)}{X(s)}\).