Question

Find the general solution for the differential equation (dy)/(dx) + 3y = 18 Y=

Answer 1

Answer:

$y=-e^{-3x-c_1}+6$

Step-by-step explanation:

$\frac{dy}{dx}+3y=18\\\\\mathrm{Substitute\quad }\frac{dy}{dx}\mathrm{\:with\:}y'\:\\\\y'\:+3y=18\\\\Rewrite\\\\\frac{1}{6-y}y'\:=3\\\\Solve \::\frac{1}{6-y}y'\:=3\\\\-In(6-y)=3x+c_1\\\\Isolate\:y\\\\\\y=-e^{-3x-c_1}+6$