I have a system that is modeled by the following differential equation:
$$db/dt = h_aj(t) + k(T_a-b(t))$$
where $db/dt$ is the rate of temperature change, $j(t)$ is an input, $h_a, k, T_a$ are all constants, and $b(t)$ is an output. Note that this is newtonian cooling with a heating input, $h_aj(t)$.
I want to find the transfer function is the Laplace domain, $B(s)/J(s)$. Taking the laplacian of the equation of interest, assuming all IC's are $0$, yields: $$sB(s)+kB(s)-\frac{kT_a}{s} = h_aJ(s).$$
What I can't figure out is the term $kT_a/s$ is not a function of $J(s)$ or $B(s)$ so I can not get a transfer function of purely $B(s)/J(s)$. Does anyone know how to solve this equation or a better way to find the transfer function relating the input to the output?