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consider $$\frac{d^2}{dx^2}(xy) - λxy=0$$. Show eigenfunctions are $$y_{n}=\frac{\sin(n\pi x)}{x}$$. Boundary conditions are y(1)=0 and y regular at x=0

I integrated twice to obtain $$6xy=λx^3y+6Ax+6B$$ where A,B constants. I can't apply the condition y is regular because I don't know what it means pratically. Besides, I can't see how I can get the required solution from this equation.

I integrated twice to obtain $$6xy=λx^3y+6Ax+6B$$ where A,B constants. I can't apply the condition y is regular because I don't know what it means pratically. Besides, I can't see how I can get the required solution from this equation.

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