Question

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

Answer 1

`y=-e^(-3x-c_1)+6`

Explanation:

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