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#### karush

##### Well-known member

- Jan 31, 2012

- 2,886

$\displaystyle \frac{dy}{dt}=ay-b$}$

(a) Find the equilibrium solution $y_e$

rewrite as

$y'-ay=b$

$\displaystyle -\exp\int a \, da=e^{a^{2}/2}$

$\color{red}{y_e=b/a}$

(b) Let $Y(t)=y-y_e$; thus $Y(t)$ is the deviation from the equilibrium solution.

Find the differential equation satisfied by $Y(t)$.

????

$\color{red}{Y' = aY}$

ok stopped in my tracks.. red is book answer