Concept:A variable separable differential equation is any differential equation in which variables can be separated. i.e. The equation which can be written in the form : \(\displaystyle N(y)\frac{dx}{dy}?=M(x)\)Formulae \(\displaystyle \int\frac{dx}{x}=ln\ x+C\)Calculation:\(\displaystyle x \frac{dy}{dx}-2y= 0\)? \(\displaystyle \frac{dy}{dx}-\frac{2y}{x}= 0\)? \(\displaystyle \frac{dy}{dx}=\frac{2y}{x}\)? \(\displaystyle \frac{dy}{y}=\frac{2dx}{x}\)By integrating both sides, we get,? \(\displaystyle \int\frac{dy}{y}=\int\frac{2dx}{x}\)? lny = 2 lnx + lnc? y = x2c? ?y = x2c represents a family of parabolas.