O.D.E Conceptual Question

I was wondering what you guys thought on this conceptual equation on O.D.E. It's something I have been struggling with, but I THINK it has something to do with linear independence. Could you chime in your two cents on the following?

http://i.imgur.com/sYSZk.jpg

Re: O.D.E Conceptual Question

(1) *True.* Choose $\displaystyle c_1=1,\;c_2=0$ and $\displaystyle c_1=0,\;c_2=1$. (2) *True.* Choose $\displaystyle y_h=0$. (3) *False.* Choose the equation $\displaystyle y'=1$, and $\displaystyle y_{p1}=x^2+x$, $\displaystyle y_{p2}=-x^2$.