ODE No. 1201

\[ x^2 y''(x)+(2 x+1) x y'(x)-4 y(x)=0 \]

✓ Mathematica : cpu = 0.260271 (sec), leaf count = 44

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

\[\left \{\left \{y(x)\to \frac {c_1 e^{-2 x} (2 x+3)}{2 x^2}+\frac {c_2 \left (2 x^2-4 x+3\right )}{4 x^2}\right \}\right \}\]

✓ Maple : cpu = 0.027 (sec), leaf count = 31

dsolve(x^2*diff(diff(y(x),x),x)+x*(2*x+1)*diff(y(x),x)-4*y(x)=0,y(x))

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