Question: Given that yi (x) = x is a solution of the second-order linear homoge- neous differential equation (2 + 22) dy da2 dy (x2

Given that yi (x) = x is a solution of the second-order

Given that yi (x) = x is a solution of the second-order linear homoge- neous differential equation (2 + 22) dy da2 dy (x2 2x - 2)y = 0, r > 0, da + x(x2 2x 2) | first state Abel's theorem and then use it to find a second solution to the above equation. Verify the second solution by substituting into the equation and finally establish the linear independence of these two solutions. [17 marks] You are required to use Abel's theorem to find a second solution, not the method of reduction of order.

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