\[ y'(x)=\frac {\sqrt {9 x^4-4 y(x)^3}+3 x^4+3 x^3}{(x+1) y(x)^2} \] ✓ Mathematica : cpu = 1.50606 (sec), leaf count = 133
DSolve[Derivative[1][y][x] == (3*x^3 + 3*x^4 + Sqrt[9*x^4 - 4*y[x]^3])/((1 + x)*y[x]^2),y[x],x]
\[\left \{\left \{y(x)\to \left (-\frac {3}{2}\right )^{2/3} \sqrt [3]{x^4-4 \log ^2(x+1)+8 c_1 \log (x+1)-4 c_1{}^2}\right \},\left \{y(x)\to \left (\frac {3}{2}\right )^{2/3} \sqrt [3]{x^4-4 \log ^2(x+1)+8 c_1 \log (x+1)-4 c_1{}^2}\right \},\left \{y(x)\to -\sqrt [3]{-1} \left (\frac {3}{2}\right )^{2/3} \sqrt [3]{x^4-4 \log ^2(x+1)+8 c_1 \log (x+1)-4 c_1{}^2}\right \}\right \}\] ✓ Maple : cpu = 0.225 (sec), leaf count = 37
dsolve(diff(y(x),x) = (3*x^4+3*x^3+(9*x^4-4*y(x)^3)^(1/2))/(1+x)/y(x)^2,y(x))
\[\int _{\textit {\_b}}^{y \left (x \right )}\frac {\textit {\_a}^{2}}{\sqrt {9 x^{4}-4 \textit {\_a}^{3}}}d \textit {\_a} -\ln \left (1+x \right )-c_{1} = 0\]