ODE No. 392

\[ y(x)^2 \log (a y(x))-x y(x) y'(x)+y'(x)^2=0 \]

✓ Mathematica : cpu = 0.227455 (sec), leaf count = 27

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

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

✓ Maple : cpu = 0.528 (sec), leaf count = 50

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

\[y \left (x \right ) = \frac {{\mathrm e}^{\frac {x^{2}}{4}}}{a}\]