\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( {a}^{3}+ \left ( y \left ( x \right ) \right ) ^{4}{a}^{3}+2\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{2}b{x}^{2}+a{x}^{4}{b}^{2}+ \left ( y \left ( x \right ) \right ) ^{6}{a}^{3}+3\, \left ( y \left ( x \right ) \right ) ^{4}{a}^{2}b{x}^{2}+3\, \left ( y \left ( x \right ) \right ) ^{2}a{b}^{2}{x}^{4}+{b}^{3}{x}^{6} \right ) x}{{a}^{7/2}y \left ( x \right ) }}=0} \]
Mathematica: cpu = 1.403178 (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 = 0.592 (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 \} \]