# Find a basis for the vector spaces of all solutions

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• March 5th 2011, 04:35 AM
cegs
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

thanks for your help.
• March 5th 2011, 05:11 AM
FernandoRevilla
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 $B=\{1,t,e^t\}$.

P.D. This kind of problems are jut routine knowing the previous theory. Have you studied it?