# What is the general solution of the differential equation # dy/dx + 2y = 0#?

##### 1 Answer

Jul 22, 2017

# y = Ce^(-2x) #

#### Explanation:

We have:

# dy/dx + 2y = 0#

We can just rearrange as follows:

# dy/dx = -2y => 1/y \ dy/dx = -2 #

This is a first Order Separable Differential Equation and "separate the variables" to get

# int \ 1/y \ dy=int \ -2 \ dx#

And integrating gives us:

# ln |y| = -2x + A #

# :. |y| = e^(-2x + A) #

Note that as

# y = e^(-2x + A) #

# \ \ = e^(-2x)e^A #

# \ \ = Ce^(-2x) #