\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( a \left ( y \left ( x \right ) \right ) ^{2}+b{x}^{2} \right ) ^{2}x}{{a}^{5/2}y \left ( x \right ) }}=0} \]
Mathematica: cpu = 0.422554 (sec), leaf count = 115 \[ \left \{\left \{y(x)\to -\sqrt {\frac {\sqrt {b} \tan \left (\frac {a^{3/2} b x^2+2 c_1}{a^{9/4} \sqrt {b}}\right )}{\sqrt [4]{a}}-\frac {b x^2}{a}}\right \},\left \{y(x)\to \sqrt {\frac {\sqrt {b} \tan \left (\frac {a^{3/2} b x^2+2 c_1}{a^{9/4} \sqrt {b}}\right )}{\sqrt [4]{a}}-\frac {b x^2}{a}}\right \}\right \} \]
Maple: cpu = 0.218 (sec), leaf count = 460 \[ \left \{ y \left ( x \right ) ={\frac {1}{a}\sqrt {- \left ( \left ( b{x} ^{2}-{a}^{{\frac {3}{2}}}\sqrt {-{b{a}^{-{\frac {3}{2}}}}} \right ) { {\rm e}^{{\frac {{x}^{2}}{2} \left ( -2\,{a}^{3/2}\sqrt {-{\frac {b}{{a }^{3/2}}}}+b{x}^{2} \right ) {a}^{-{\frac {3}{2}}}}}}+{\it \_C1}\, \left ( {a}^{{\frac {3}{2}}}\sqrt {-{b{a}^{-{\frac {3}{2}}}}}+b{x}^{2} \right ) {{\rm e}^{{\frac {{x}^{2}}{2} \left ( 2\,{a}^{3/2}\sqrt {-{ \frac {b}{{a}^{3/2}}}}+b{x}^{2} \right ) {a}^{-{\frac {3}{2}}}}}} \right ) a \left ( {\it \_C1}\,{{\rm e}^{{\frac {{x}^{2}}{2} \left ( 2\, {a}^{3/2}\sqrt {-{\frac {b}{{a}^{3/2}}}}+b{x}^{2} \right ) {a}^{-{ \frac {3}{2}}}}}}+{{\rm e}^{{\frac {{x}^{2}}{2} \left ( -2\,{a}^{3/2} \sqrt {-{\frac {b}{{a}^{3/2}}}}+b{x}^{2} \right ) {a}^{-{\frac {3}{2}}} }}} \right ) } \left ( {\it \_C1}\,{{\rm e}^{{\frac {{x}^{2}}{2} \left ( 2\,{a}^{3/2}\sqrt {-{\frac {b}{{a}^{3/2}}}}+b{x}^{2} \right ) {a}^{-{ \frac {3}{2}}}}}}+{{\rm e}^{{\frac {{x}^{2}}{2} \left ( -2\,{a}^{3/2} \sqrt {-{\frac {b}{{a}^{3/2}}}}+b{x}^{2} \right ) {a}^{-{\frac {3}{2}}} }}} \right ) ^{-1}},y \left ( x \right ) =-{\frac {1}{a}\sqrt {- \left ( \left ( b{x}^{2}-{a}^{{\frac {3}{2}}}\sqrt {-{b{a}^{-{\frac {3}{2}}}}} \right ) {{\rm e}^{{\frac {{x}^{2}}{2} \left ( -2\,{a}^{3/2}\sqrt {-{ \frac {b}{{a}^{3/2}}}}+b{x}^{2} \right ) {a}^{-{\frac {3}{2}}}}}}+{\it \_C1}\, \left ( {a}^{{\frac {3}{2}}}\sqrt {-{b{a}^{-{\frac {3}{2}}}}}+b {x}^{2} \right ) {{\rm e}^{{\frac {{x}^{2}}{2} \left ( 2\,{a}^{3/2} \sqrt {-{\frac {b}{{a}^{3/2}}}}+b{x}^{2} \right ) {a}^{-{\frac {3}{2}}} }}} \right ) a \left ( {\it \_C1}\,{{\rm e}^{{\frac {{x}^{2}}{2} \left ( 2\,{a}^{3/2}\sqrt {-{\frac {b}{{a}^{3/2}}}}+b{x}^{2} \right ) {a}^{-{ \frac {3}{2}}}}}}+{{\rm e}^{{\frac {{x}^{2}}{2} \left ( -2\,{a}^{3/2} \sqrt {-{\frac {b}{{a}^{3/2}}}}+b{x}^{2} \right ) {a}^{-{\frac {3}{2}}} }}} \right ) } \left ( {\it \_C1}\,{{\rm e}^{{\frac {{x}^{2}}{2} \left ( 2\,{a}^{3/2}\sqrt {-{\frac {b}{{a}^{3/2}}}}+b{x}^{2} \right ) {a}^{-{ \frac {3}{2}}}}}}+{{\rm e}^{{\frac {{x}^{2}}{2} \left ( -2\,{a}^{3/2} \sqrt {-{\frac {b}{{a}^{3/2}}}}+b{x}^{2} \right ) {a}^{-{\frac {3}{2}}} }}} \right ) ^{-1}} \right \} \]