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The differential equation (e^(-2√(x))/√(x) - y/√(x)) (dx)/(dy) = 1 has the solution

1. y e^(2√(x)) = 2√(x) + c
2. y e^(-2√(x)) = √(x) + c
3. y = √(x)
4. y = 3√(x)

Correct answer: y e^(2√(x)) = 2√(x) + c

Solution

Rearranging gives sqrt(x) dy/dx + y = e^(-2sqrt x), i.e. dy/dx + y/sqrt x = e^(-2sqrt x)/sqrt x. The integrating factor is e^(2sqrt x), and the solution is y*e^(2sqrt x) = 2sqrt(x) + C.

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