Question: Consider (x ^2 )y '' 4x y' + 6y = 0 for x > 0. We know y1(x) = x^2 is a solution. Find another

Consider (x ^2 )y '' 4x y' + 6y = 0 for x > 0. We know y1(x) = x^2 is a solution. Find another solution to the equation by using the method of reduction of order and then find the value of b (with b > 0) so that the following boundary value problem has non-trivial solutions

(x^2 )y '' 4x y' +6y = 0, y(1) = 0, y ' (b) = 0.

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