Consider the equation d²u dx² P₂(x)- du dx + P₁(x). + po(x)u = 0. dx y By introducing a new function y(x) by u = exp (f dr. the Riccati equation dy Po P1 - y². dx P2 P2 show that Y satisfies The general solution of the second-order equation for u has two arbitrary constants. The general solution of the first-order equation for y has one arbitrary constant. Explain how this contradiction can be resolved.

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