Question

y'=36y+72

find general solution to the equation.

Answer 1

$y'=36y+72$
$y'-36y=72$
$e^{-36t}y'-36e^{-36t}y=72e^{-36t}$
$\dfrac{\mathrm d}{\mathrm dt}[e^{-36t}y]=72e^{-36t}$
$e^{-36t}y=72\displaystyle\int e^{-36t}\,\mathrm dt$
$e^{-36t}y=-2e^{-36t}+C$
$y=-2+Ce^{36t}$