# Math Help - Find a basis for the vector spaces of all solutions

1. ## Find a basis for the vector spaces of all solutions

Find a basis for the vector spaces of all solutions of y'''-3y''=0 y'=dy/dt

2. The roots of the characteistic equation $\lambda^3-\lambda^2=0$ are $\lambda=0$ (double) and $\lambda=1$ (simple) so, a basis for the vector space of all solutions is $B=\{1,t,e^t\}$.