\[ y'(x)=\frac {x \left (a y(x)^2+b x^2\right )^3}{a^{5/2} y(x) \left (a y(x)^2+a+b x^2\right )} \] ✓ Mathematica : cpu = 2.82513 (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 = 1.072 (sec), leaf count = 400
\[ \left \{ \int _{{\it \_b}}^{x}\!{\frac { \left ( {{\it \_a}}^{2}b+a \left ( y \left ( x \right ) \right ) ^{2} \right ) ^{3}{\it \_a}}{{a}^{3}} \left ( \left ( y \left ( x \right ) \right ) ^{6}{a}^{3}+3\,{a}^{2}b{{\it \_a}}^{2} \left ( y \left ( x \right ) \right ) ^{4}+3\,a{b}^{2}{{\it \_a}}^{4} \left ( y \left ( x \right ) \right ) ^{2}+{b}^{3}{{\it \_a}}^{6}+{a}^{{\frac {5}{2}}}b \left ( y \left ( x \right ) \right ) ^{2}+{a}^{{\frac {3}{2}}}{b}^{2}{{\it \_a}}^{2}+{a}^{{\frac {5}{2}}}b \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!-{ \left ( {{\it \_f}}^{2}a+b{x}^{2}+a \right ) {\it \_f}{\frac {1}{\sqrt {a}}} \left ( {a}^{3}{{\it \_f}}^{6}+3\,{a}^{2}b{x}^{2}{{\it \_f}}^{4}+3\,a{b}^{2}{x}^{4}{{\it \_f}}^{2}+{b}^{3}{x}^{6}+{a}^{{\frac {5}{2}}}b{{\it \_f}}^{2}+{a}^{{\frac {3}{2}}}{b}^{2}{x}^{2}+{a}^{{\frac {5}{2}}}b \right ) ^{-1}}-\int _{{\it \_b}}^{x}\!-{\frac { \left ( {{\it \_a}}^{2}b+{{\it \_f}}^{2}a \right ) ^{3}{\it \_a}}{{a}^{3}} \left ( 6\,{a}^{3}{{\it \_f}}^{5}+12\,{a}^{2}b{{\it \_a}}^{2}{{\it \_f}}^{3}+6\,a{b}^{2}{{\it \_a}}^{4}{\it \_f}+2\,{a}^{5/2}b{\it \_f} \right ) \left ( {a}^{3}{{\it \_f}}^{6}+3\,{a}^{2}b{{\it \_a}}^{2}{{\it \_f}}^{4}+3\,a{b}^{2}{{\it \_a}}^{4}{{\it \_f}}^{2}+{b}^{3}{{\it \_a}}^{6}+{a}^{{\frac {5}{2}}}b{{\it \_f}}^{2}+{a}^{{\frac {3}{2}}}{b}^{2}{{\it \_a}}^{2}+{a}^{{\frac {5}{2}}}b \right ) ^{-2}}+6\,{\frac { \left ( {{\it \_a}}^{2}b+{{\it \_f}}^{2}a \right ) ^{2}{\it \_a}\,{\it \_f}}{{a}^{2} \left ( {a}^{3}{{\it \_f}}^{6}+3\,{a}^{2}b{{\it \_a}}^{2}{{\it \_f}}^{4}+3\,a{b}^{2}{{\it \_a}}^{4}{{\it \_f}}^{2}+{b}^{3}{{\it \_a}}^{6}+{a}^{5/2}b{{\it \_f}}^{2}+{a}^{3/2}{b}^{2}{{\it \_a}}^{2}+{a}^{5/2}b \right ) }}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \} \]