differential equation

Question

Write and then solve the differential equation for the statement: "The rate of change of y with respect to x is inversely proportional to the square root of y."

Answer 1

The words translate into dy/dx = k/√x;

 

equivalently, by cross multiplication, √y dy = k dx;

 

 

antidifferentiation gives (2/3) y^(3/2) = kx + C