Find a basis for the vector spaces of all solutions of y'''-3y''=0 y'=dy/dt
thanks for your help.
The roots of the characteistic equation $\displaystyle \lambda^3-\lambda^2=0$ are $\displaystyle \lambda=0$ (double) and $\displaystyle \lambda=1$ (simple) so, a basis for the vector space of all solutions is $\displaystyle B=\{1,t,e^t\}$.
P.D. This kind of problems are jut routine knowing the previous theory. Have you studied it?