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(b) For the Sturm-Liouville ODE p (2 ). dy dx + q(2) y(2) + Ar(a)y=0 dx show that it is always possible to find a

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(b) For the Sturm-Liouville ODE p (2 ). dy dx + q(2) y(2) + Ar(a)y=0 dx show that it is always possible to find a function x = g(() such that when expressed in terms of the variable ( the resulting Sturm-Liouville ODE takes the form d d B(5) dy dc + C(S)y (5) + dy (5) = 0 Determine B and C in terms of p, q and g. This shows that it is always pos- sible to find a variable transformation that transforms a given Sturm-Liouville problem to one where the coefficient function modifying the eigenvalue 1 is one

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