Find the solution to the differential equation dy/dx + y/3 = 0 subject to conditions y(0)= 6?

1 Answer
Mar 7, 2018

#y = e^(-1/3x)+5#

Explanation:

This type of equation is separable. So we want to place #x#'s and #y#'s on opposite sides of the equal sign and combine them with their respective differentials.

#dy/dx + y/3 = 0#

#dy/dx = -y/3#

#1/ydy = -1/3dx#

Integrate both sides:

#\int1/ydy = -1/3\intdx#

#ln(y) = -1/3x+C# ; where #C \equiv# constant

#y = e^(-1/3x)+C# ; C is a constant, so it can arbitrarily absorb other constants.

We can use the point (0,6) given to us:
#6 = e^(-1/3(0)) + C#

#C = 5#

Hence: #y = e^(-1/3x)+5#