Find the particular solution of the differential equation dy

Find the particular solution of the differential equation dy/dx + 2y = 8 satisfying the initial condition y(0)=0

y=???

dy/dx = 8-2y or, (1/(8-2y))dy = dx integrating both the sides- (-1/2)ln(8-2y) = x + c x=0, y=0 (-1/2)ln8 = c so, ln(8-2y) = -2x -2c or, ln(8-2y) = -2x + ln8 (8-2y) = e^(ln8 - 2x) 8 - e^(ln8-2x) = 2y y = 4 - (1/2) e^(ln8-2x)