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

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Answer 1 · 2016-07-11T14:51:48

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

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

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

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

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

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

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

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

and if you like

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

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