differential equation?

Question

I need to find the solution to the differential equation,
dy/dx=sqrt(y/x). I need to solve it for y. This is where I'm at
dy(sqrt (y))=dx(sqrt(x)). Where do I go from here> what do I do with the dy and dx when I take the antiderivitive. Please help me solve for y.

Answer 1

You have an error in your 2nd equation. It should read
dy/sqrt(y) = dx/sqrt(x)
Then
∫dy/sqrt(y) = ∫dx/sqrt(x)
2sqrt(y) = 2sqrt(x) + C
sqrt(y) = sqrt(x) + C
y = (sqrt(x) + C)^2 = x +2Csqrt(x) + C^2

Answer 2

You just integrate both sides- the dx and dy go away:

sqrt[y] dy = sqrt[x] dx

2/3 y^ 3/2 = 2/3 x^ 3/2 + C

y ^ 3/2 = x^ 3/2 + C

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