ODE No. 1128

\[ (x f(x)+2) y'(x)+f(x) y(x)+x y''(x)=0 \] Mathematica : cpu = 0.020017 (sec), leaf count = 40

DSolve[f[x]*y[x] + (2 + x*f[x])*Derivative[1][y][x] + x*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \frac {c_2 \int _1^x\exp \left (-\int _1^{K[2]}f(K[1])dK[1]\right )dK[2]}{x}+\frac {c_1}{x}\right \}\right \}\] Maple : cpu = 0.195 (sec), leaf count = 32

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

\[y \left (x \right ) = \frac {c_{2} \left (\int {\mathrm e}^{\int \frac {-x f \left (x \right )-2}{x}d x} x^{2}d x \right )+c_{1}}{x}\]