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I need the solution of the question 3. Q1. Find a power series solution in powers...

I need the solution of the question 3.

Q1. Find a power series solution in powers of x.

y''+(1+x^2)y=0

Q2. Find a solution of (1-x^2)y''-2xy'+n(n+1)y=0 by reduction to the Legendre equation.

Q3. Find a basis of solutions. Try to identify the series as expansions of known functions.

(1) xy''+2y'-xy=0

(2) (x^2+x)y''+(4x+2)y'+2y=0

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