\[ y'(x)=\frac {x \left (a^3 y(x)^6+a^3 y(x)^4+a^3+3 a^2 b x^2 y(x)^4+2 a^2 b x^2 y(x)^2+3 a b^2 x^4 y(x)^2+a b^2 x^4+b^3 x^6\right )}{a^{7/2} y(x)} \] ✓ Mathematica : cpu = 1.09102 (sec), leaf count = 164
DSolve[Derivative[1][y][x] == (x*(a^3 + a*b^2*x^4 + b^3*x^6 + 2*a^2*b*x^2*y[x]^2 + 3*a*b^2*x^4*y[x]^2 + a^3*y[x]^4 + 3*a^2*b*x^2*y[x]^4 + a^3*y[x]^6))/(a^(7/2)*y[x]),y[x],x]
\[\text {Solve}\left [\frac {x^2}{2}-\frac {1}{2} a^{5/2} \text {RootSum}\left [\text {$\#$1}^3 b^3+3 \text {$\#$1}^2 a b^2 y(x)^2+\text {$\#$1}^2 a b^2+3 \text {$\#$1} a^2 b y(x)^4+2 \text {$\#$1} a^2 b y(x)^2+a^{5/2} b+a^3 y(x)^6+a^3 y(x)^4+a^3\& ,\frac {\log \left (x^2-\text {$\#$1}\right )}{3 \text {$\#$1}^2 b^2+6 \text {$\#$1} a b y(x)^2+2 \text {$\#$1} a b+3 a^2 y(x)^4+2 a^2 y(x)^2}\& \right ]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.642 (sec), leaf count = 352
dsolve(diff(y(x),x) = (a^3+y(x)^4*a^3+2*y(x)^2*a^2*b*x^2+a*x^4*b^2+y(x)^6*a^3+3*y(x)^4*a^2*b*x^2+3*y(x)^2*a*b^2*x^4+b^3*x^6)*x/a^(7/2)/y(x),y(x))
\[\int _{\textit {\_b}}^{x}\frac {\left (b^{3} \textit {\_a}^{6}+3 y \left (x \right )^{2} a \,b^{2} \textit {\_a}^{4}+3 y \left (x \right )^{4} a^{2} b \,\textit {\_a}^{2}+y \left (x \right )^{6} a^{3}+a \,\textit {\_a}^{4} b^{2}+2 a^{2} y \left (x \right )^{2} b \,\textit {\_a}^{2}+y \left (x \right )^{4} a^{3}+a^{3}\right ) \textit {\_a}}{\left (y \left (x \right )^{6} a^{3}+3 y \left (x \right )^{4} a^{2} b \,\textit {\_a}^{2}+3 y \left (x \right )^{2} a \,b^{2} \textit {\_a}^{4}+b^{3} \textit {\_a}^{6}+y \left (x \right )^{4} a^{3}+2 a^{2} y \left (x \right )^{2} b \,\textit {\_a}^{2}+a \,\textit {\_a}^{4} b^{2}+a^{3}+a^{\frac {5}{2}} b \right ) a^{\frac {7}{2}}}d \textit {\_a} +\int _{}^{y \left (x \right )}\left (-\frac {\textit {\_f}}{\textit {\_f}^{6} a^{3}+3 \textit {\_f}^{4} a^{2} b \,x^{2}+3 \textit {\_f}^{2} a \,b^{2} x^{4}+b^{3} x^{6}+a^{3} \textit {\_f}^{4}+2 a^{2} \textit {\_f}^{2} b \,x^{2}+a \,x^{4} b^{2}+a^{3}+a^{\frac {5}{2}} b}-\left (\int _{\textit {\_b}}^{x}\frac {6 b \textit {\_f} \left (\textit {\_a}^{2} b +a \,\textit {\_f}^{2}\right ) \left (a \,\textit {\_f}^{2}+\textit {\_a}^{2} b +\frac {2}{3} a \right ) \textit {\_a}}{\left (a^{\frac {5}{2}} b +\left (\textit {\_f}^{6}+\textit {\_f}^{4}+1\right ) a^{3}+3 \left (\textit {\_f}^{2}+\frac {2}{3}\right ) b \,\textit {\_f}^{2} \textit {\_a}^{2} a^{2}+3 \left (\textit {\_f}^{2}+\frac {1}{3}\right ) b^{2} \textit {\_a}^{4} a +b^{3} \textit {\_a}^{6}\right )^{2}}d \textit {\_a} \right )\right )d \textit {\_f} +c_{1} = 0\]