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What is a solution to the differential equation #dy/dy=sqrt(x/y)#?

Answer 1

William Abdalla

# y^(3/2) = x^(3/2) + C#

and if you like

# y = ( x^(3/2) + C)^(2/3)#

assuming firstly this is a typo and that you meant to say #dy/color{red}{dx}#

if so, separate it

#dy/dx=sqrt(x/y)#

#sqrt y dy/dx=sqrt(x)#

#int \ sqrt y dy/dx \ dx =int sqrt(x) \ dx#

#int \ sqrt y \ dy =int sqrt(x) \ dx#

power rule

#2/3 y^(3/2) = 2/3 x^(3/2) + C#

# y^(3/2) = x^(3/2) + C#

and if you like

# y = ( x^(3/2) + C)^(2/3)#

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Answer 2

Evelyn Agard

The solution to the differential equation dy/dx = sqrt(x/y) is given by the implicit equation: 2y^(3/2)/3 = x + 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.