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What is a solution to the differential equation #dy/dx=xe^y#?

Answer 1

Cameron Alexander

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

#y' = xe^y#

#e^(-y)y' = x#

#int e^(-y)y' dx =int x dx#

#int e^(-y) dy =int x dx#

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

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

# -y =ln (C - x^2/2) #

# y =- ln (C - x^2/2) #

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

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Answer 2

Emily Ammerman

The solution to the differential equation dy/dx = xe^y is y = ln(|C + 0.5x^2 + 1|), 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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