$To$ solve the separable differential equation

$\frac{dy}{dx}=9y$

$we$ must find two separate integrals:

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}},dy=$

and

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}},dx=$

Solving for $ywe$ get that $y=$

$(you$ must use $kas$ your constant$)$

and find the particular solution satisfying the initial condition

$y(0)=-9$

$y(x)=$