\[ f(x) \left (x^2 y''(x)-2 x y'(x)+2 y(x)\right )+y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.0924054 (sec), leaf count = 88
DSolve[f[x]*(2*y[x] - 2*x*Derivative[1][y][x] + x^2*Derivative[2][y][x]) + Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_3 x \left (\int _1^x\frac {\exp \left (-\int _1^{K[2]}f(K[1]) K[1]^2dK[1]\right )}{K[2]^2}dK[2]-x \int _1^x\frac {\exp \left (-\int _1^{K[3]}f(K[1]) K[1]^2dK[1]\right )}{K[3]^3}dK[3]\right )+c_2 x^2+c_1 x\right \}\right \}\] ✓ Maple : cpu = 0.143 (sec), leaf count = 33
dsolve(diff(diff(diff(y(x),x),x),x)+f(x)*(x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+2*y(x))=0,y(x))
\[y \left (x \right ) = \left (\int \left (c_{1}+c_{2} \left (\int {\mathrm e}^{-\left (\int \left (x^{2} f \left (x \right )+\frac {3}{x}\right )d x \right )}d x \right )\right )d x +c_{3}\right ) x\]