\[ y'(x)=\frac {x \left (a y(x)^2+b x^2\right )^2}{a^{5/2} y(x)} \] ✓ Mathematica : cpu = 0.417613 (sec), leaf count = 115
\[\left \{\left \{y(x)\to -\sqrt {-\frac {b x^2}{a}+\frac {\sqrt {b} \tan \left (\frac {a^{3/2} b x^2+2 c_1}{a^{9/4} \sqrt {b}}\right )}{\sqrt [4]{a}}}\right \},\left \{y(x)\to \sqrt {-\frac {b x^2}{a}+\frac {\sqrt {b} \tan \left (\frac {a^{3/2} b x^2+2 c_1}{a^{9/4} \sqrt {b}}\right )}{\sqrt [4]{a}}}\right \}\right \}\] ✓ Maple : cpu = 0.302 (sec), leaf count = 460
\[\left \{y \left (x \right ) = \frac {\sqrt {-\left (c_{1} \left (b \,x^{2}+\sqrt {-\frac {b}{a^{\frac {3}{2}}}}\, a^{\frac {3}{2}}\right ) {\mathrm e}^{\frac {\left (b \,x^{2}+2 \sqrt {-\frac {b}{a^{\frac {3}{2}}}}\, a^{\frac {3}{2}}\right ) x^{2}}{2 a^{\frac {3}{2}}}}+\left (b \,x^{2}-\sqrt {-\frac {b}{a^{\frac {3}{2}}}}\, a^{\frac {3}{2}}\right ) {\mathrm e}^{\frac {\left (b \,x^{2}-2 \sqrt {-\frac {b}{a^{\frac {3}{2}}}}\, a^{\frac {3}{2}}\right ) x^{2}}{2 a^{\frac {3}{2}}}}\right ) \left (c_{1} {\mathrm e}^{\frac {\left (b \,x^{2}+2 \sqrt {-\frac {b}{a^{\frac {3}{2}}}}\, a^{\frac {3}{2}}\right ) x^{2}}{2 a^{\frac {3}{2}}}}+{\mathrm e}^{\frac {\left (b \,x^{2}-2 \sqrt {-\frac {b}{a^{\frac {3}{2}}}}\, a^{\frac {3}{2}}\right ) x^{2}}{2 a^{\frac {3}{2}}}}\right ) a}}{\left (c_{1} {\mathrm e}^{\frac {\left (b \,x^{2}+2 \sqrt {-\frac {b}{a^{\frac {3}{2}}}}\, a^{\frac {3}{2}}\right ) x^{2}}{2 a^{\frac {3}{2}}}}+{\mathrm e}^{\frac {\left (b \,x^{2}-2 \sqrt {-\frac {b}{a^{\frac {3}{2}}}}\, a^{\frac {3}{2}}\right ) x^{2}}{2 a^{\frac {3}{2}}}}\right ) a}, y \left (x \right ) = -\frac {\sqrt {-\left (c_{1} \left (b \,x^{2}+\sqrt {-\frac {b}{a^{\frac {3}{2}}}}\, a^{\frac {3}{2}}\right ) {\mathrm e}^{\frac {\left (b \,x^{2}+2 \sqrt {-\frac {b}{a^{\frac {3}{2}}}}\, a^{\frac {3}{2}}\right ) x^{2}}{2 a^{\frac {3}{2}}}}+\left (b \,x^{2}-\sqrt {-\frac {b}{a^{\frac {3}{2}}}}\, a^{\frac {3}{2}}\right ) {\mathrm e}^{\frac {\left (b \,x^{2}-2 \sqrt {-\frac {b}{a^{\frac {3}{2}}}}\, a^{\frac {3}{2}}\right ) x^{2}}{2 a^{\frac {3}{2}}}}\right ) \left (c_{1} {\mathrm e}^{\frac {\left (b \,x^{2}+2 \sqrt {-\frac {b}{a^{\frac {3}{2}}}}\, a^{\frac {3}{2}}\right ) x^{2}}{2 a^{\frac {3}{2}}}}+{\mathrm e}^{\frac {\left (b \,x^{2}-2 \sqrt {-\frac {b}{a^{\frac {3}{2}}}}\, a^{\frac {3}{2}}\right ) x^{2}}{2 a^{\frac {3}{2}}}}\right ) a}}{\left (c_{1} {\mathrm e}^{\frac {\left (b \,x^{2}+2 \sqrt {-\frac {b}{a^{\frac {3}{2}}}}\, a^{\frac {3}{2}}\right ) x^{2}}{2 a^{\frac {3}{2}}}}+{\mathrm e}^{\frac {\left (b \,x^{2}-2 \sqrt {-\frac {b}{a^{\frac {3}{2}}}}\, a^{\frac {3}{2}}\right ) x^{2}}{2 a^{\frac {3}{2}}}}\right ) a}\right \}\]