The answer above is NOT correct. Consider the equation (1-3x^(2))y^('')+6xy^(')-6y=0 Suppose that you somehow guessed that y=x is a solution. Use the reduction of order method to find a second linearly independent solution, and solve the initial value problem with y(0)=3,y^(')(0)=3 y= help (formulas). Book: Section 2.1 of Notes on Diffy Qs

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