What is a solution to the differential equation #dy/dx=e^(x+y)#?

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Steve M Share
Nov 16, 2016

Answer:

# y = -ln(-e^x + C) #, or #ln(1/(C-e^x))#

Explanation:

# dy/dx = e^(x+y) #
# :. dy/dx = e^xe^y #

So we can identify this as a First Order Separable Differential Equation. We can therefore "separate the variables" to give:

# int 1/e^y dy = int e^x dx#
# :. int e^-y dy = int e^x dx#

Integrating gives us:

# -e^-y = e^x + C' #
# :. e^-y = -e^x + C #
# :. -y = ln(-e^x + C) #
# :. y = -ln(C-e^x) #, or #ln(1/(C-e^x))#

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