What is a solution to the differential equation #dy/dx=3x^2e^-y#?

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Answer 1 · 2016-07-14T09:00:06

#y=ln (x^3 + C)#

#dy/dx=3x^2e^-y#

separate it

#e^y dy/dx=3x^2#

#int \ e^y dy/dx \ dx=int \ 3x^2 \ dx#

#int \ e^y \ dy=int \ 3x^2 \ dx#

#e^y=x^3 + C#

#y=ln (x^3 + C)#