\[ y'(x)=\frac {x \left (a^3 y(x)^6+a^3 y(x)^4+a^3+3 a^2 b x^2 y(x)^4+2 a^2 b x^2 y(x)^2+3 a b^2 x^4 y(x)^2+a b^2 x^4+b^3 x^6\right )}{a^{7/2} y(x)} \] ✓ Mathematica : cpu = 1.37261 (sec), leaf count = 164
\[\text {Solve}\left [\frac {x^2}{2}-\frac {1}{2} a^{5/2} \text {RootSum}\left [\text {$\#$1}^3 b^3+3 \text {$\#$1}^2 a b^2 y(x)^2+\text {$\#$1}^2 a b^2+3 \text {$\#$1} a^2 b y(x)^4+2 \text {$\#$1} a^2 b y(x)^2+a^{5/2} b+a^3 y(x)^6+a^3 y(x)^4+a^3\& ,\frac {\log \left (x^2-\text {$\#$1}\right )}{3 \text {$\#$1}^2 b^2+6 \text {$\#$1} a b y(x)^2+2 \text {$\#$1} a b+3 a^2 y(x)^4+2 a^2 y(x)^2}\& \right ]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.68 (sec), leaf count = 352
\[\left \{c_{1}+\int _{\textit {\_b}}^{x}\frac {\left (\textit {\_a}^{6} b^{3}+3 \textit {\_a}^{4} a \,b^{2} y \left (x \right )^{2}+3 \textit {\_a}^{2} a^{2} b y \left (x \right )^{4}+a^{3} y \left (x \right )^{6}+\textit {\_a}^{4} a \,b^{2}+2 \textit {\_a}^{2} a^{2} b y \left (x \right )^{2}+a^{3} y \left (x \right )^{4}+a^{3}\right ) \textit {\_a}}{\left (\textit {\_a}^{6} b^{3}+3 \textit {\_a}^{4} a \,b^{2} y \left (x \right )^{2}+3 \textit {\_a}^{2} a^{2} b y \left (x \right )^{4}+a^{3} y \left (x \right )^{6}+\textit {\_a}^{4} a \,b^{2}+2 \textit {\_a}^{2} a^{2} b y \left (x \right )^{2}+a^{3} y \left (x \right )^{4}+a^{\frac {5}{2}} b +a^{3}\right ) a^{\frac {7}{2}}}d \textit {\_a} +\int _{}^{y \left (x \right )}\left (-\frac {\textit {\_f}}{\textit {\_f}^{6} a^{3}+3 \textit {\_f}^{4} a^{2} b \,x^{2}+3 \textit {\_f}^{2} a \,b^{2} x^{4}+b^{3} x^{6}+\textit {\_f}^{4} a^{3}+2 \textit {\_f}^{2} a^{2} b \,x^{2}+a \,b^{2} x^{4}+a^{\frac {5}{2}} b +a^{3}}-\left (\int _{\textit {\_b}}^{x}\frac {6 \left (\textit {\_a}^{2} b +\textit {\_f}^{2} a \right ) \left (\textit {\_a}^{2} b +\textit {\_f}^{2} a +\frac {2}{3} a \right ) \textit {\_a} \textit {\_f} b}{\left (\textit {\_a}^{6} b^{3}+3 \left (\textit {\_f}^{2}+\frac {1}{3}\right ) \textit {\_a}^{4} a \,b^{2}+3 \left (\textit {\_f}^{2}+\frac {2}{3}\right ) \textit {\_a}^{2} \textit {\_f}^{2} a^{2} b +a^{\frac {5}{2}} b +\left (\textit {\_f}^{6}+\textit {\_f}^{4}+1\right ) a^{3}\right )^{2}}d \textit {\_a} \right )\right )d \textit {\_f} = 0\right \}\]