ODE No. 1199

\[ x^2 y''(x)-(x+4) x y'(x)+4 y(x)=0 \] Mathematica : cpu = 0.0128615 (sec), leaf count = 41

DSolve[4*y[x] - x*(4 + x)*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_2 e^x x^4-\frac {1}{6} c_1 x \left (e^x x^3 \text {Ei}(-x)+x^2-x+2\right )\right \}\right \}\] Maple : cpu = 0.016 (sec), leaf count = 35

dsolve(x^2*diff(diff(y(x),x),x)-x*(x+4)*diff(y(x),x)+4*y(x)=0,y(x))
 

\[y \left (x \right ) = \left (\Ei \left (1, x\right ) {\mathrm e}^{x} c_{2} x^{3}+c_{1} x^{3} {\mathrm e}^{x}-c_{2} \left (x^{2}-x +2\right )\right ) x\]