\[ -4 a^2 x y'(x)+a^2 y(x)+y(x) y'(x)^2=0 \] ✓ Mathematica : cpu = 2.58955 (sec), leaf count = 753
DSolve[a^2*y[x] - 4*a^2*x*Derivative[1][y][x] + y[x]*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\text {Solve}\left [\frac {8 \left (4 a^2-\frac {y(x)^2}{x^2}\right )^{3/2} \text {arcsinh}\left (\frac {\sqrt {\frac {y(x)}{x}-2 a}}{2 \sqrt {a}}\right )+\sqrt {a} \sqrt {\frac {y(x)}{a x}+2} \left (\sqrt {-\left (\frac {y(x)}{x}-2 a\right )^2} \sqrt {2 a+\frac {y(x)}{x}} \sqrt {4 a^2-\frac {y(x)^2}{x^2}} \left (\log \left (3 a^2-\frac {y(x)^2}{x^2}\right )-8 \arctan \left (\frac {\sqrt {2 a-\frac {y(x)}{x}}}{\sqrt {2 a+\frac {y(x)}{x}}}\right )+4 \log \left (\frac {y(x)}{x}\right )\right )+4 \sqrt {\frac {y(x)}{x}-2 a} \left (\frac {y(x)^2}{x^2}-4 a^2\right ) \text {arctanh}\left (\frac {\sqrt {4 a^2-\frac {y(x)^2}{x^2}}}{2 a}\right )-2 \sqrt {\frac {y(x)}{x}-2 a} \left (\frac {y(x)^2}{x^2}-4 a^2\right ) \text {arctanh}\left (\frac {\sqrt {4 a^2-\frac {y(x)^2}{x^2}}}{a}\right )\right )}{6 \sqrt {a} \sqrt {-\left (\frac {y(x)}{x}-2 a\right )^2} \sqrt {2 a+\frac {y(x)}{x}} \sqrt {\frac {y(x)}{a x}+2} \sqrt {4 a^2-\frac {y(x)^2}{x^2}}}=-\log (x)+c_1,y(x)\right ],\text {Solve}\left [\frac {\sqrt {a} \sqrt {\frac {y(x)}{a x}+2} \left (\sqrt {-\left (\frac {y(x)}{x}-2 a\right )^2} \sqrt {2 a+\frac {y(x)}{x}} \sqrt {4 a^2-\frac {y(x)^2}{x^2}} \left (\log \left (3 a^2-\frac {y(x)^2}{x^2}\right )+8 \arctan \left (\frac {\sqrt {2 a-\frac {y(x)}{x}}}{\sqrt {2 a+\frac {y(x)}{x}}}\right )+4 \log \left (\frac {y(x)}{x}\right )\right )-4 \sqrt {\frac {y(x)}{x}-2 a} \left (\frac {y(x)^2}{x^2}-4 a^2\right ) \text {arctanh}\left (\frac {\sqrt {4 a^2-\frac {y(x)^2}{x^2}}}{2 a}\right )+2 \sqrt {\frac {y(x)}{x}-2 a} \left (\frac {y(x)^2}{x^2}-4 a^2\right ) \text {arctanh}\left (\frac {\sqrt {4 a^2-\frac {y(x)^2}{x^2}}}{a}\right )\right )-8 \left (4 a^2-\frac {y(x)^2}{x^2}\right )^{3/2} \text {arcsinh}\left (\frac {\sqrt {\frac {y(x)}{x}-2 a}}{2 \sqrt {a}}\right )}{6 \sqrt {a} \sqrt {-\left (\frac {y(x)}{x}-2 a\right )^2} \sqrt {2 a+\frac {y(x)}{x}} \sqrt {\frac {y(x)}{a x}+2} \sqrt {4 a^2-\frac {y(x)^2}{x^2}}}=-\log (x)+c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.087 (sec), leaf count = 181
dsolve(y(x)*diff(y(x),x)^2-4*a^2*x*diff(y(x),x)+a^2*y(x) = 0,y(x))
\[-\frac {c_{1} x}{y \left (x \right ) a \left (\frac {a^{2} \left (2 a^{2} x^{2}+\sqrt {4 a^{2} x^{2}-y \left (x \right )^{2}}\, a x -y \left (x \right )^{2}\right )}{y \left (x \right )^{2}}\right )^{\frac {1}{3}} {\left (\frac {\left (2 a x +\sqrt {4 a^{2} x^{2}-y \left (x \right )^{2}}\right ) a}{y \left (x \right )}\right )}^{\frac {1}{3}}}+x = 0\]