y1 =x and y2=x^2 Find an equation of the form y'' + p(x)y' + q(x)y=0 for which y1,y2 are solutions. The solutions our lecturer gave us say q=2/x^2 and p= -2/x Although, he did not show how to derive them. Any help? Thanks.
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Just substitute both 'solutions' into the d.e., that gets you two equations in p and q which can be solved simultaneously.
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