\[ 3 a y(x)^3+6 a x y(x)^2+y'(x)=0 \] ✓ Mathematica : cpu = 0.309808 (sec), leaf count = 185
DSolve[6*a*x*y[x]^2 + 3*a*y[x]^3 + Derivative[1][y][x] == 0,y[x],x]
\[\text {Solve}\left [\frac {\sqrt [3]{-3} \sqrt [3]{a} x \operatorname {AiryAi}\left ((-3)^{2/3} a^{2/3} x^2-\frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )+\operatorname {AiryAiPrime}\left ((-3)^{2/3} a^{2/3} x^2-\frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )}{\sqrt [3]{-3} \sqrt [3]{a} x \operatorname {AiryBi}\left ((-3)^{2/3} a^{2/3} x^2-\frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )+\operatorname {AiryBiPrime}\left ((-3)^{2/3} a^{2/3} x^2-\frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )}+c_1=0,y(x)\right ]\] ✓ Maple : cpu = 0.039 (sec), leaf count = 48
dsolve(diff(y(x),x)+3*a*y(x)^3+6*a*x*y(x)^2 = 0,y(x))
\[y \left (x \right ) = \frac {1}{3 a \,x^{2}+\operatorname {RootOf}\left (\left (-3 a \right )^{\frac {1}{3}} \operatorname {AiryBi}\left (\textit {\_Z} \right ) c_{1} x +\left (-3 a \right )^{\frac {1}{3}} x \operatorname {AiryAi}\left (\textit {\_Z} \right )+\operatorname {AiryBi}\left (1, \textit {\_Z}\right ) c_{1}+\operatorname {AiryAi}\left (1, \textit {\_Z}\right )\right ) \left (-3 a \right )^{\frac {1}{3}}}\]