Chapter 1.6, Problem 41P

Program Plan Intro

Program Description: Purpose of problem is to show that the differential equation $\left(\frac{2x}{y}-\frac{3y^2}{x^4}\right)dx+\left(\frac{2y}{x^3}-\frac{x^2}{y^2}+\frac{1}{\sqrt{y}}\right)dy=0$ is exact and obtain the solution for it.

Summary introduction: If the differential equation is $M\left(x,y\right)dx+N\left(x,y\right)dy=0$ then the below condition must satisfies,

  $\frac{\partial M}{dy}=\frac{\partial N}{\partial x}$ ....... (1)