ODE
\[ (x f(x)+2) y'(x)+f(x) y(x)+x y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.211402 (sec), leaf count = 0 , could not solve
DSolve[f[x]*y[x] + (2 + x*f[x])*Derivative[1][y][x] + x*Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.28 (sec), leaf count = 32
\[ \left \{ y \left ( x \right ) ={\frac {1}{x} \left ( {\it \_C2}\,\int \!{{\rm e}^{\int \!{\frac {-2-xf \left ( x \right ) }{x}}\,{\rm d}x}}{x}^{2}\,{\rm d}x+{\it \_C1} \right ) } \right \} \] Mathematica raw input
DSolve[f[x]*y[x] + (2 + x*f[x])*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[f[x]*y[x] + (2 + x*f[x])*Derivative[1][y][x] + x*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+(2+x*f(x))*diff(y(x),x)+f(x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C2*Int(exp(Int((-2-x*f(x))/x,x))*x^2,x)+_C1)/x