Question: Use the method of eigenfunction expansions to solve the problems: a. (y^{prime prime}+4 y=x^{2}, quad y^{prime}(0)=y^{prime}(1)=0). b. (y+4 y=x^{2} quad y(0)=y(1)=0).

Use the method of eigenfunction expansions to solve the problems:

a. \(y^{\prime \prime}+4 y=x^{2}, \quad y^{\prime}(0)=y^{\prime}(1)=0\).

b. \(y+4 y=x^{2} \quad y(0)=y(1)=0\).

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