Chapter 1.6, Problem 42P

Program Plan Intro

Program Description: Purpose of problem is to showthat the differential equation $\frac{2x^{\frac{5}{2}}-3y^{\frac{5}{3}}}{2x^{\frac{5}{2}}{y}^{\frac{2}{3}}}dx+\frac{3y^{\frac{5}{3}}-2x^{\frac{5}{2}}}{3x^{\frac{3}{2}}{y}^{\frac{5}{3}}}dy=0$ 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)