I have just completed a section on Second ODE and Second Order Linear Homogenous equations. Topics were the superposition principle, the wronskian, and linear dependence and independence.

But Part A of this exercise question is not clear to me.

Given the diff equ

a) Show that the equation has a linear polynomial and a quadratic polynomial as solutions. ??

b) Find two linearly independent solutions of the equation and find the general solution. (For this do i assume the answer is in the form )

Any clarification to help get me started is appreciated. Thanks.