Find the equation of the curve with the derivative of y with respect to x given as (2/√x)-x, passing through the point (2,1)

Question

Hi, can anybody help me with the following question? "Find the equation of the curve with the derivative of y with respect to x given as (2/√x)-x, passing through the point (2,1)"

Answer 1

y = ∫y'dx = ∫(2/√x - x)dx

 

y = 2∫x^-½dx - ∫xdx

 

y = 4√x - ½x² + C

 

Since (2,1) lies on the curve, y = 1 when x = 2.

 

So, 1 = 4√2 - 2 + C

 

     C = 3 - 4√2

 

y = 4√x - ½x² + 3 - 4√2