\[ y'(x)=\frac {x \left (a y(x)^2+b x^2\right )^3}{a^{5/2} y(x) \left (a y(x)^2+a+b x^2\right )} \] ✓ Mathematica : cpu = 3.0744 (sec), leaf count = 1
\[\{\}\]
✓ Maple : cpu = 1.023 (sec), leaf count = 246
\[ \left \{ \int _{{\it \_b}}^{x}\!{\frac { \left ( {{\it \_a}}^{2}b+a \left ( y \left ( x \right ) \right ) ^{2} \right ) ^{3}{\it \_a}}{{a}^{3}} \left ( b \left ( \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) {a}^{{\frac {5}{2}}}+{a}^{{\frac {3}{2}}}{b}^{2}{{\it \_a}}^{2}+ \left ( {{\it \_a}}^{2}b+a \left ( y \left ( x \right ) \right ) ^{2} \right ) ^{3} \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!{1 \left ( \left ( \left ( -{{\it \_f}}^{2}-1 \right ) b{a}^{{\frac {5}{2}}}-{a}^{{\frac {3}{2}}}{b}^{2}{x}^{2}- \left ( {{\it \_f}}^{2}a+b{x}^{2} \right ) ^{3} \right ) \int _{{\it \_b}}^{x}\!4\,{\frac { \left ( {{\it \_f}}^{2}a+{{\it \_a}}^{2}b+3/2\,a \right ) {\it \_a}\, \left ( {{\it \_a}}^{2}b+{{\it \_f}}^{2}a \right ) ^{2}{\it \_f}\,b}{\sqrt {a} \left ( b \left ( {{\it \_f}}^{2}+1 \right ) {a}^{5/2}+{a}^{3/2}{b}^{2}{{\it \_a}}^{2}+ \left ( {{\it \_a}}^{2}b+{{\it \_f}}^{2}a \right ) ^{3} \right ) ^{2}}}\,{\rm d}{\it \_a}-{ \left ( {{\it \_f}}^{2}a+b{x}^{2}+a \right ) {\it \_f}{\frac {1}{\sqrt {a}}}} \right ) \left ( b \left ( {{\it \_f}}^{2}+1 \right ) {a}^{{\frac {5}{2}}}+{a}^{{\frac {3}{2}}}{b}^{2}{x}^{2}+ \left ( {{\it \_f}}^{2}a+b{x}^{2} \right ) ^{3} \right ) ^{-1}}{d{\it \_f}}+{\it \_C1}=0 \right \} \]