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OpenStudy (anonymous):
ok here's a tough differential equation question: if the functions y1 and y2 are linearly independent solutions of y'' + p(x)y' + q(x)y=0 under what conditions (eg for which values of a1,b1,a2,b2) the functions y3=a1y1+a2y2 and y4=b1y1+b2y2 also form a linearly independent set of solutions.
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