ODE No. 1127

\[ y(x) \left (a^2 x \log ^2(x)+a \log (x)+a\right )+(2 a x \log (x)+1) y'(x)+x y''(x)=0 \]

✓ Mathematica : cpu = 0.0237825 (sec), leaf count = 36

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

\[\left \{\left \{y(x)\to c_1 e^{a x} x^{-a x}+c_2 e^{a x} x^{-a x} \log (x)\right \}\right \}\]

✓ Maple : cpu = 0.04 (sec), leaf count = 21

dsolve(x*diff(diff(y(x),x),x)+(2*a*x*ln(x)+1)*diff(y(x),x)+(a^2*x*ln(x)^2+a*ln(x)+a)*y(x)=0,y(x))

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