Solve the D.E : U''-2xU' +2u = 0

Do I write out the series solution or write somthing like : C1e^r1 + c2e^r2 ,for r1&r2 are the roots of the equation~ What is the different between these two answer?

One more question,

Q2 : Show function (arcsin x )^2 satisfies

(1-x^2)U'' - xU' = 2 /For U(0) = 0; U'(0) = 0

Can write out few steps for me please?