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

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Answer 1 · 2017-06-12T15:02:03

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

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 #e^x > 0 AA x in RR#, we can write the solution as:

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