\[ y(x)^3 \left (4 a^2 x+3 a x^2+b\right )+y'(x)+3 x y(x)^2=0 \] ✓ Mathematica : cpu = 4.05225 (sec), leaf count = 490
DSolve[3*x*y[x]^2 + (b + 4*a^2*x + 3*a*x^2)*y[x]^3 + Derivative[1][y][x] == 0,y[x],x]
\[\text {Solve}\left [c_1=-\frac {i \sqrt {-\frac {4 a^3-3 b}{4 a^3}-\frac {3}{2 a^2 y(x)}+\frac {(-2 a-3 x)^2}{4 a^2}} \operatorname {BesselJ}\left (\frac {1}{2} \sqrt {\frac {4 a^3-3 b}{a^3}}+1,-i \sqrt {\frac {(-2 a-3 x)^2}{4 a^2}-\frac {4 a^3-3 b}{4 a^3}-\frac {3}{2 a^2 y(x)}}\right )+\left (\frac {1}{2} \sqrt {\frac {4 a^3-3 b}{a^3}}+\frac {-2 a-3 x}{2 a}\right ) \operatorname {BesselJ}\left (\frac {1}{2} \sqrt {\frac {4 a^3-3 b}{a^3}},-i \sqrt {\frac {(-2 a-3 x)^2}{4 a^2}-\frac {4 a^3-3 b}{4 a^3}-\frac {3}{2 a^2 y(x)}}\right )}{i \sqrt {-\frac {4 a^3-3 b}{4 a^3}-\frac {3}{2 a^2 y(x)}+\frac {(-2 a-3 x)^2}{4 a^2}} \operatorname {BesselY}\left (\frac {1}{2} \sqrt {\frac {4 a^3-3 b}{a^3}}+1,-i \sqrt {\frac {(-2 a-3 x)^2}{4 a^2}-\frac {4 a^3-3 b}{4 a^3}-\frac {3}{2 a^2 y(x)}}\right )+\left (\frac {1}{2} \sqrt {\frac {4 a^3-3 b}{a^3}}+\frac {-2 a-3 x}{2 a}\right ) \operatorname {BesselY}\left (\frac {1}{2} \sqrt {\frac {4 a^3-3 b}{a^3}},-i \sqrt {\frac {(-2 a-3 x)^2}{4 a^2}-\frac {4 a^3-3 b}{4 a^3}-\frac {3}{2 a^2 y(x)}}\right )},y(x)\right ]\] ✓ Maple : cpu = 1.075 (sec), leaf count = 373
dsolve(diff(y(x),x)+(4*a^2*x+3*a*x^2+b)*y(x)^3+3*x*y(x)^2 = 0,y(x))
\[c_{1}+\frac {-\operatorname {BesselK}\left (\frac {\sqrt {\frac {4 a^{3}-3 b}{a^{3}}}}{2}+1, -\frac {\sqrt {3}\, \sqrt {\frac {4 y \left (x \right ) a^{2} x +3 y \left (x \right ) a \,x^{2}+b y \left (x \right )-2 a}{a^{3} y \left (x \right )}}}{2}\right ) \sqrt {3}\, \sqrt {\frac {4 y \left (x \right ) a^{2} x +3 y \left (x \right ) a \,x^{2}+b y \left (x \right )-2 a}{a^{3} y \left (x \right )}}\, a -\left (a \sqrt {\frac {4 a^{3}-3 b}{a^{3}}}-2 a -3 x \right ) \operatorname {BesselK}\left (\frac {\sqrt {\frac {4 a^{3}-3 b}{a^{3}}}}{2}, -\frac {\sqrt {3}\, \sqrt {\frac {4 y \left (x \right ) a^{2} x +3 y \left (x \right ) a \,x^{2}+b y \left (x \right )-2 a}{a^{3} y \left (x \right )}}}{2}\right )}{\operatorname {BesselI}\left (\frac {\sqrt {\frac {4 a^{3}-3 b}{a^{3}}}}{2}+1, -\frac {\sqrt {3}\, \sqrt {\frac {4 y \left (x \right ) a^{2} x +3 y \left (x \right ) a \,x^{2}+b y \left (x \right )-2 a}{a^{3} y \left (x \right )}}}{2}\right ) \sqrt {3}\, \sqrt {\frac {4 y \left (x \right ) a^{2} x +3 y \left (x \right ) a \,x^{2}+b y \left (x \right )-2 a}{a^{3} y \left (x \right )}}\, a -\left (a \sqrt {\frac {4 a^{3}-3 b}{a^{3}}}-2 a -3 x \right ) \operatorname {BesselI}\left (\frac {\sqrt {\frac {4 a^{3}-3 b}{a^{3}}}}{2}, -\frac {\sqrt {3}\, \sqrt {\frac {4 y \left (x \right ) a^{2} x +3 y \left (x \right ) a \,x^{2}+b y \left (x \right )-2 a}{a^{3} y \left (x \right )}}}{2}\right )} = 0\]