\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( a \left ( y \left ( x \right ) \right ) ^{2}+b{x}^{2} \right ) ^{3}x}{{a}^{5/2} \left ( a \left ( y \left ( x \right ) \right ) ^{2}+b{x}^{2}+a \right ) y \left ( x \right ) }}=0} \]
Mathematica: cpu = 3.705971 (sec), leaf count = 175 \[ \text {Solve}\left [\frac {1}{2} \left (x^2-a^{3/2} \text {RootSum}\left [\text {$\#$1}^3 b^3+3 \text {$\#$1}^2 a b^2 y(x)^2+\text {$\#$1} a^{3/2} b^2+3 \text {$\#$1} a^2 b y(x)^4+a^{5/2} b y(x)^2+a^{5/2} b+a^3 y(x)^6\& ,\frac {a y(x)^2 \log \left (x^2-\text {$\#$1}\right )+a \log \left (x^2-\text {$\#$1}\right )+\text {$\#$1} b \log \left (x^2-\text {$\#$1}\right )}{3 \text {$\#$1}^2 b^2+6 \text {$\#$1} a b y(x)^2+a^{3/2} b+3 a^2 y(x)^4}\& \right ]\right )=c_1,y(x)\right ] \]
Maple: cpu = 0.749 (sec), leaf count = 400 \[ \left \{ \int _{{\it \_b}}^{x}\!{\frac { \left ( b{{\it \_a}}^{2}+a \left ( y \left ( x \right ) \right ) ^{2} \right ) ^{3}{\it \_a}}{{a}^{3 }} \left ( \left ( y \left ( x \right ) \right ) ^{6}{a}^{3}+3\,{a}^{2}b{ {\it \_a}}^{2} \left ( y \left ( x \right ) \right ) ^{4}+3\,a{b}^{2}{{ \it \_a}}^{4} \left ( y \left ( x \right ) \right ) ^{2}+{b}^{3}{{\it \_a }}^{6}+{a}^{{\frac {5}{2}}}b \left ( y \left ( x \right ) \right ) ^{2}+{ a}^{{\frac {3}{2}}}{b}^{2}{{\it \_a}}^{2}+{a}^{{\frac {5}{2}}}b \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!-{ \left ( a{{\it \_f}}^{2}+b{x}^{2}+a \right ) {\it \_f}{\frac {1}{\sqrt {a}}} \left ( {a}^{3}{{\it \_f}}^{6}+3\,{a}^{2}b{x}^{2}{{\it \_f}}^{4}+ 3\,a{b}^{2}{x}^{4}{{\it \_f}}^{2}+{b}^{3}{x}^{6}+{a}^{{\frac {5}{2}}}b {{\it \_f}}^{2}+{a}^{{\frac {3}{2}}}{b}^{2}{x}^{2}+{a}^{{\frac {5}{2}} }b \right ) ^{-1}}-\int _{{\it \_b}}^{x}\!-{\frac { \left ( b{{\it \_a}}^ {2}+a{{\it \_f}}^{2} \right ) ^{3}{\it \_a}}{{a}^{3}} \left ( 6\,{a}^{3} {{\it \_f}}^{5}+12\,{a}^{2}b{{\it \_a}}^{2}{{\it \_f}}^{3}+6\,a{b}^{2} {{\it \_a}}^{4}{\it \_f}+2\,{a}^{5/2}b{\it \_f} \right ) \left ( {a}^{3 }{{\it \_f}}^{6}+3\,{a}^{2}b{{\it \_a}}^{2}{{\it \_f}}^{4}+3\,a{b}^{2} {{\it \_a}}^{4}{{\it \_f}}^{2}+{b}^{3}{{\it \_a}}^{6}+{a}^{{\frac {5}{ 2}}}b{{\it \_f}}^{2}+{a}^{{\frac {3}{2}}}{b}^{2}{{\it \_a}}^{2}+{a}^{{ \frac {5}{2}}}b \right ) ^{-2}}+6\,{\frac { \left ( b{{\it \_a}}^{2}+a{{ \it \_f}}^{2} \right ) ^{2}{\it \_a}\,{\it \_f}}{{a}^{2} \left ( {a}^{3} {{\it \_f}}^{6}+3\,{a}^{2}b{{\it \_a}}^{2}{{\it \_f}}^{4}+3\,a{b}^{2}{ {\it \_a}}^{4}{{\it \_f}}^{2}+{b}^{3}{{\it \_a}}^{6}+{a}^{5/2}b{{\it \_f}}^{2}+{a}^{3/2}{b}^{2}{{\it \_a}}^{2}+{a}^{5/2}b \right ) }} \,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \} \]