Chapter 1.6, Problem 44P

Program Plan Intro

Program Description: Purpose of problem is to calculate the second-order differential equation $y{y}^{″}+{\left(y^{\prime }\right)}^2=0$ .

Summary introduction: The general form of second order differential equation with independent variable $x$ missing is $F\left(y,y^{\prime },y^{″}\right)=0$ .

Substitute the below expression that results in first order differential equation as $p=\frac{dy}{dx}$ or $y^{″}=\frac{dp}{dy}$ . The first-order differential equation is $F\left(x,p,p\frac{dp}{dy}\right)=0$ .