Is $y = \frac { a } { b } + C e ^ { - b t }$ the general solution to the differential equation $\frac { d y } { d t } = a - b y$ ?

Question

Quizplus · Accepted Answer

The given differential equation is a first-order linear ordinary differential equation (ODE) of the form $\frac{dy}{dt} + by = a$. The solution provided, $y = \frac{a}{b} + Ce^{-bt}$, correctly represents the general solution to this ODE, where $\frac{a}{b}$ is the steady-state solution and $Ce^{-bt}$ represents the transient solution that decays over time.

Is y=ab+Ce−bty = \frac { a } { b } + C e ^ { - b t }y=ba​+Ce−bt

Is $y = \frac { a } { b } + C e ^ { - b t }$