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Solve the Differential Equation

Which of the following is a solution to the differential equation:
ylny + xy' = 0 for x > 0 ?

A. xlny = 1 B. xylny = 1 C. (lny)2 = 2
D. -y(lny)(lnx) = 1 E. lny + (x2/2)y = 1

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The answer is A.

A. xlny=1, then (xlny)'=0, then lny+(x/y)y'=0. We multiply y on both sides and get
ylny+xy'=0. ...

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A Differential Equation is solved. The solution is detailed and well presented. The response was given a rating of "5" by the student who originally posted the question.

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