Solution to second order ODE with non-negative loadings

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I have found many references to general solutions of ODEs of the form $$ ay(x)''+by(x)'+cy(x)=0, $$ and outlined "methods" for the case where $a,b,c$ are non-constant. If I were to assume that $b=0$ and $a,c$ are positive functions of x then is there a known explicit general solution?