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

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Answer 1 · 2017-10-07T00:39:41

# y = 6e^x -4 #

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, #y=2# when #x=0# we have:

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

Leading to the PS:

# y = 6e^x -4 #