Hi guys, really stuck on this one, help would be greatly appreciated=)

After finding the dimension of the vector space A,give a basis for A.

$\displaystyle A=${$\displaystyle p(x)$in $\displaystyle P_2$: $\displaystyle xp'(x)=p(x)$}

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- Aug 2nd 2010, 12:36 PMjames12vector space/basis
Hi guys, really stuck on this one, help would be greatly appreciated=)

After finding the dimension of the vector space A,give a basis for A.

$\displaystyle A=${$\displaystyle p(x)$in $\displaystyle P_2$: $\displaystyle xp'(x)=p(x)$} - Aug 2nd 2010, 12:57 PMlvleph
You will want to solve the DEQ using separation of variables. This will give a family of solutions. You can then probably see the basis.

- Aug 2nd 2010, 03:33 PMjames12
Ok thanks, got it now. basis will just be x and dimension will be 1

- Aug 2nd 2010, 03:41 PMlvleph
Sounds right to me.