\[ y'(x)=\frac {\sqrt {4 y(x)^3-9 x^4}+3 x^3+x^3 \sqrt {4 y(x)^3-9 x^4}+x^2 \sqrt {4 y(x)^3-9 x^4}}{y(x)^2} \] ✓ Mathematica : cpu = 2.94794 (sec), leaf count = 266
\[\left \{\left \{y(x)\to -\frac {1}{2} \sqrt [3]{-\frac {1}{2}} \sqrt [3]{9 x^8+24 x^7+16 x^6+72 x^5+114 x^4+72 c_1 x^4-24 x^3+96 c_1 x^3+144 x^2-72 x+288 c_1 x+9+144 c_1{}^2-72 c_1}\right \},\left \{y(x)\to \frac {\sqrt [3]{9 x^8+24 x^7+16 x^6+72 x^5+114 x^4+72 c_1 x^4-24 x^3+96 c_1 x^3+144 x^2-72 x+288 c_1 x+9+144 c_1{}^2-72 c_1}}{2 \sqrt [3]{2}}\right \},\left \{y(x)\to \frac {(-1)^{2/3} \sqrt [3]{9 x^8+24 x^7+16 x^6+72 x^5+114 x^4+72 c_1 x^4-24 x^3+96 c_1 x^3+144 x^2-72 x+288 c_1 x+9+144 c_1{}^2-72 c_1}}{2 \sqrt [3]{2}}\right \}\right \}\] ✓ Maple : cpu = 0.213 (sec), leaf count = 44
\[\int _{\textit {\_b}}^{y \relax (x )}\frac {\textit {\_a}^{2}}{\sqrt {-9 x^{4}+4 \textit {\_a}^{3}}}d \textit {\_a} -\frac {x^{4}}{4}-\frac {x^{3}}{3}-x -c_{1} = 0\]