ODE No. 1205

\[ a x^2 y'(x)+f(x) y(x)+x^2 y''(x)=0 \] Mathematica : cpu = 0.242396 (sec), leaf count = 0

DSolve[f[x]*y[x] + a*x^2*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
 

, could not solve

DSolve[f[x]*y[x] + a*x^2*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0, y[x], x]

Maple : cpu = 0. (sec), leaf count = 0

dsolve(x^2*diff(diff(y(x),x),x)+a*x^2*diff(y(x),x)+f(x)*y(x)=0,y(x))
 

, result contains DESol or ODESolStruc

\[y \left (x \right ) = \mathit {DESol}\left (\left \{\frac {f \left (x \right ) \textit {\_Y} \left (x \right )}{x^{2}}+a \left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right )+\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\]