# What is the general solution of the differential equation? # dy/dx=y(1+e^x) #

##### 1 Answer

Jun 12, 2017

# y = Ae^(x+e^x) #

#### Explanation:

We have:

# dy/dx=y(1+e^x) #

This is a first Order Separable Differential Equation, we can collect terms by rearranging the equation as follows

# 1/y dy/dx=(1+e^x) #

And now we can "separate the variables" to get

# int \ 1/y \ dy = int \ 1+e^x \ dx #

And integrating gives us:

# ln|y| = x+e^x + C #

# :. |y| = e^(x+e^x + C) #

# :. |y| = e^(x+e^x) e^C #

And as

# :. y = Ae^(x+e^x) #