\[ y'(x)=\frac {x \left (a^3 y(x)^6+a^3 y(x)^4+a^3+3 a^2 b x^2 y(x)^4+2 a^2 b x^2 y(x)^2+3 a b^2 x^4 y(x)^2+a b^2 x^4+b^3 x^6\right )}{a^{7/2} y(x)} \] ✓ Mathematica : cpu = 1.43115 (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 = 0.811 (sec), leaf count = 595
\[ \left \{ \int _{{\it \_b}}^{x}\!{ \left ( {b}^{3}{{\it \_a}}^{6}+3\, \left ( y \left ( x \right ) \right ) ^{2}a{b}^{2}{{\it \_a}}^{4}+3\, \left ( y \left ( x \right ) \right ) ^{4}{a}^{2}b{{\it \_a}}^{2}+ \left ( y \left ( x \right ) \right ) ^{6}{a}^{3}+a{{\it \_a}}^{4}{b}^{2}+2\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{2}b{{\it \_a}}^{2}+ \left ( y \left ( x \right ) \right ) ^{4}{a}^{3}+{a}^{3} \right ) {\it \_a} \left ( \left ( y \left ( x \right ) \right ) ^{6}{a}^{3}+3\, \left ( y \left ( x \right ) \right ) ^{4}{a}^{2}b{{\it \_a}}^{2}+3\, \left ( y \left ( x \right ) \right ) ^{2}a{b}^{2}{{\it \_a}}^{4}+{b}^{3}{{\it \_a}}^{6}+ \left ( y \left ( x \right ) \right ) ^{4}{a}^{3}+2\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{2}b{{\it \_a}}^{2}+a{{\it \_a}}^{4}{b}^{2}+{a}^{3}+{a}^{{\frac {5}{2}}}b \right ) ^{-1}{a}^{-{\frac {7}{2}}}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!-{{\it \_f} \left ( {{\it \_f}}^{6}{a}^{3}+3\,{{\it \_f}}^{4}{a}^{2}b{x}^{2}+3\,{{\it \_f}}^{2}a{b}^{2}{x}^{4}+{b}^{3}{x}^{6}+{{\it \_f}}^{4}{a}^{3}+2\,{{\it \_f}}^{2}{a}^{2}b{x}^{2}+a{x}^{4}{b}^{2}+{a}^{3}+{a}^{{\frac {5}{2}}}b \right ) ^{-1}}-\int _{{\it \_b}}^{x}\!{ \left ( 6\,{{\it \_a}}^{4}{\it \_f}\,a{b}^{2}+12\,{{\it \_a}}^{2}{{\it \_f}}^{3}{a}^{2}b+6\,{{\it \_f}}^{5}{a}^{3}+4\,{{\it \_a}}^{2}{\it \_f}\,{a}^{2}b+4\,{{\it \_f}}^{3}{a}^{3} \right ) {\it \_a} \left ( {{\it \_f}}^{6}{a}^{3}+3\,{{\it \_f}}^{4}{a}^{2}b{{\it \_a}}^{2}+3\,{{\it \_f}}^{2}a{b}^{2}{{\it \_a}}^{4}+{b}^{3}{{\it \_a}}^{6}+{{\it \_f}}^{4}{a}^{3}+2\,{{\it \_f}}^{2}{a}^{2}b{{\it \_a}}^{2}+a{{\it \_a}}^{4}{b}^{2}+{a}^{3}+{a}^{{\frac {5}{2}}}b \right ) ^{-1}{a}^{-{\frac {7}{2}}}}-{ \left ( {b}^{3}{{\it \_a}}^{6}+3\,{{\it \_f}}^{2}a{b}^{2}{{\it \_a}}^{4}+3\,{{\it \_f}}^{4}{a}^{2}b{{\it \_a}}^{2}+{{\it \_f}}^{6}{a}^{3}+a{{\it \_a}}^{4}{b}^{2}+2\,{{\it \_f}}^{2}{a}^{2}b{{\it \_a}}^{2}+{{\it \_f}}^{4}{a}^{3}+{a}^{3} \right ) {\it \_a}\, \left ( 6\,{{\it \_a}}^{4}{\it \_f}\,a{b}^{2}+12\,{{\it \_a}}^{2}{{\it \_f}}^{3}{a}^{2}b+6\,{{\it \_f}}^{5}{a}^{3}+4\,{{\it \_a}}^{2}{\it \_f}\,{a}^{2}b+4\,{{\it \_f}}^{3}{a}^{3} \right ) \left ( {{\it \_f}}^{6}{a}^{3}+3\,{{\it \_f}}^{4}{a}^{2}b{{\it \_a}}^{2}+3\,{{\it \_f}}^{2}a{b}^{2}{{\it \_a}}^{4}+{b}^{3}{{\it \_a}}^{6}+{{\it \_f}}^{4}{a}^{3}+2\,{{\it \_f}}^{2}{a}^{2}b{{\it \_a}}^{2}+a{{\it \_a}}^{4}{b}^{2}+{a}^{3}+{a}^{{\frac {5}{2}}}b \right ) ^{-2}{a}^{-{\frac {7}{2}}}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \} \]