# What is the general solution of the differential equation #dy/dx=6e^x#?

##### 1 Answer

Oct 7, 2017

#### Explanation:

We have:

# dy/dx=6e^x #

This is a FIrst Order Separable ODE so we can just separate the variables to get:

# int \ dy = int \ 6e^x \ dx#

Both sides are directly integrable so if we integrate we get:

# y = 6e^x + C#

Applying the initial Conditions,

# 2 = 6e^0 + C => C = -4 #

Leading to the PS:

# y = 6e^x -4 #