- #1

karush

Gold Member

MHB

- 3,269

- 5

1000

$\textsf{Consider the differential equation

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

(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

$\textsf{Consider the differential equation

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

(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

Last edited: