\[ 2 a^2 x+2 x^2 y'(x)-2 y(x)^2-3 x y(x)=0 \] ✓ Mathematica : cpu = 0.142898 (sec), leaf count = 131
DSolve[2*a^2*x - 3*x*y[x] - 2*y[x]^2 + 2*x^2*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {x^2 \left (-\frac {e^{\frac {2 a}{\sqrt {x}}}}{4 a \sqrt {x}}+\frac {e^{\frac {2 a}{\sqrt {x}}}}{2 x}+c_1 \left (\frac {a e^{-\frac {2 a}{\sqrt {x}}}}{x}+\frac {e^{-\frac {2 a}{\sqrt {x}}}}{2 \sqrt {x}}\right )\right )}{-\frac {\sqrt {x} e^{\frac {2 a}{\sqrt {x}}}}{2 a}+c_1 \sqrt {x} e^{-\frac {2 a}{\sqrt {x}}}}\right \}\right \}\] ✓ Maple : cpu = 0.201 (sec), leaf count = 100
dsolve(2*x^2*diff(y(x),x)-2*y(x)^2-3*x*y(x)+2*a^2*x = 0,y(x))
\[y \left (x \right ) = \frac {-x \left (c_{1}-2 \sqrt {-\frac {a^{2}}{x}}\right ) \cos \left (2 \sqrt {-\frac {a^{2}}{x}}\right )-2 \sin \left (2 \sqrt {-\frac {a^{2}}{x}}\right ) x \left (c_{1} \sqrt {-\frac {a^{2}}{x}}+\frac {1}{2}\right )}{2 \cos \left (2 \sqrt {-\frac {a^{2}}{x}}\right ) c_{1}+2 \sin \left (2 \sqrt {-\frac {a^{2}}{x}}\right )}\]