What is a solution to the differential equation #(dy/dx) - y - e^(3x) = 0#?

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Answer 1 · 2016-07-11T20:50:52

# y = 1/2 e^(3x) + Ce^x#

#dy/dx - y - e^(3x) = 0#

this is not separable so we use an Integrating Factor (IF)

#dy/dx - y = e^(3x) #

#IF = e^{int (-1) dx} = e^-x#

#implies e^-x dy/dx - e^-x y = e^(2x) #

Or #d/dx ( e^-x y )= e^(2x) #

# e^-x y = int \ e^(2x) \ dx#

# e^-x y = 1/2 e^(2x) + C#

# y = 1/2 e^(3x) + Ce^x#