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

Answer 1

Emily Ammerman

#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)#

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Answer 2

William Abdalla

The solution to the differential equation dy/dx = 3x^2e^(-y) is given by:

ln|e^y| = x^3 + C

Where C is the constant of integration.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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