Answer
a) $y_e=\frac{b}{a}$
b) $dy/dt=aY$
Work Step by Step
a) The equilibrium solution is the solution when $dy/dt=ay-b=0$.
So, $dy/dt=0=ay_e-b$.n therefore $ay=b$, therefore $y=\frac{b}{a}$
b)find the differential equation satisfied by $Y(t)$ if $Y(t)=y-y_e$.arrange the given equation as $Y(t)+y_e=y$, plug this into the equation for $dy/dt$ so $dy/dt=a(Y(t)+y_e)-b$, and $y_e=b/a$. This means that $dy/dt=a(Y(t)+b/a)-b$ therefore $dy/dt=aY(t)+b-b$ therefore $dy/dt=aY(t)$
