Consider the equation ( $\displaystyle E_3 $) y''' - p(x)y = 0. Prove that if y is a solution of ($\displaystyle E_3 $) satisfying y(a) = y'(a)=0 and y''(a)> 0, then y(x)>0, y'(x)>0, y''>0 on (a, inifinty) if p(x) is a postive continous function. Can a solution of ( $\displaystyle E_3 $) have a 2-1 distribution?

Can someone break this down for me so I can know what to do??