\[ y'(x)=\frac {x \left (a y(x)^2+b x^2\right )^3}{a^{5/2} y(x) \left (a y(x)^2+a+b x^2\right )} \] ✓ Mathematica : cpu = 2.93149 (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 = 1.05 (sec), leaf count = 246
\[ \left \{ \int _{{\it \_b}}^{x}\!{\frac { \left ( {{\it \_a}}^{2}b+a \left ( y \left ( x \right ) \right ) ^{2} \right ) ^{3}{\it \_a}}{{a}^{3}} \left ( b \left ( \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) {a}^{{\frac {5}{2}}}+{a}^{{\frac {3}{2}}}{b}^{2}{{\it \_a}}^{2}+ \left ( {{\it \_a}}^{2}b+a \left ( y \left ( x \right ) \right ) ^{2} \right ) ^{3} \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!{1 \left ( \left ( \left ( -{{\it \_f}}^{2}-1 \right ) b{a}^{{\frac {5}{2}}}-{a}^{{\frac {3}{2}}}{b}^{2}{x}^{2}- \left ( {{\it \_f}}^{2}a+b{x}^{2} \right ) ^{3} \right ) \int _{{\it \_b}}^{x}\!4\,{\frac {{\it \_a}\,b \left ( {{\it \_f}}^{2}a+{{\it \_a}}^{2}b+3/2\,a \right ) {\it \_f}\, \left ( {{\it \_a}}^{2}b+{{\it \_f}}^{2}a \right ) ^{2}}{\sqrt {a} \left ( b \left ( {{\it \_f}}^{2}+1 \right ) {a}^{5/2}+{a}^{3/2}{b}^{2}{{\it \_a}}^{2}+ \left ( {{\it \_a}}^{2}b+{{\it \_f}}^{2}a \right ) ^{3} \right ) ^{2}}}\,{\rm d}{\it \_a}-{ \left ( {{\it \_f}}^{2}a+b{x}^{2}+a \right ) {\it \_f}{\frac {1}{\sqrt {a}}}} \right ) \left ( b \left ( {{\it \_f}}^{2}+1 \right ) {a}^{{\frac {5}{2}}}+{a}^{{\frac {3}{2}}}{b}^{2}{x}^{2}+ \left ( {{\it \_f}}^{2}a+b{x}^{2} \right ) ^{3} \right ) ^{-1}}{d{\it \_f}}+{\it \_C1}=0 \right \} \]