Is the given function phi(x) = x^2 - x^-1 an explicit solution to the linear equation d^2y/dx^2 - 2/x^2 y = 0? Circle your answer. (a) yes (b) no

Answer:YesStep-by-step explanation:We are given that a function [tex]\phi(x)=x^2-x^{-1}[/tex]We have to find that given function is an explicit solution to the linear equation[tex]\frac{d^2y}{dx^2}-\frac{2}{x^2}y=0[/tex]If given function is an explicit solution of given linear equation then it satisfied the given differential equationDifferentiate w.r.t xThen we get [tex]\phi'(x)=2x+x^{-2}[/tex]Again differentiate w.r.t xThen we get [tex]\phi''(x)=2-\frac{2}{x^3}[/tex]Substitute all values in the given differential equation[tex]2-\frac{2}{x^3}-\frac{2}{x^2}(x^2-x^{-1})[/tex]=[tex]2-\frac{2}{x^3}-2+\frac{2}{x^3}=0[/tex]Hence, given function is an explicit solution of given differential equation.Therefore, answer is yes.