O Extend the method to a variable-coefficient ODE + p2(x)y" + P1(x)y' + po(x)y = 0. Assuming a solution yi to be known, show that another solution is y2(x) = u(x)y1(x) with u(x) = z obtained by solving Sz(x) dx and %3D yız" + (3yi + p2yı)z' + (3yi + 2p2yí + p1y1)z = 0. b) x3y" - 3x2y" + (6 – x³>xy' – (6 – x)y = 0, Reduce using v, = x (perhans obtainable bv inspection).

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