Most general way to solve second order differential equation
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This equation can not be solved in terms of elementary functions nor classical special functions. By this I mean the homogeneous counterpart, since once the homogeneous equation is solved, the nonhomogeneous one can also be solved, at least in quadratures.
Solvable cases correspond to particular choices of a(x),b(x),c(x)a(x),b(x),c(x). One way to understand if you are in such a special situation is to analyze the structure of singular points of the equation in the extended complex plane of xx. This is an algorithmic procedure.
Solvable cases correspond to particular choices of a(x),b(x),c(x)a(x),b(x),c(x). One way to understand if you are in such a special situation is to analyze the structure of singular points of the equation in the extended complex plane of xx. This is an algorithmic procedure.
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