\[ y'(x)=\frac {-2 a^{3/2} b x^2 y(x)^2+2 a^{3/2} c y(x)^2+a^{5/2} y(x)^4+\sqrt {a} b^2 x^4-2 \sqrt {a} b c x^2+\sqrt {a} c^2+b x^3}{a x^2 y(x)} \] ✓ Mathematica : cpu = 1.31015 (sec), leaf count = 236
\[\left \{\left \{y(x)\to -\frac {\sqrt {2 a^{5/2} b x^2-2 a^{5/2} c+4 a^3 b^2 x^3-4 a^3 b c x+a^2 x+4 \sqrt {a} b^2 c_1 x^2-4 \sqrt {a} b c c_1+2 b c_1 x}}{\sqrt {2} \sqrt {2 a^{3/2} b c_1+a^{7/2}+2 a^4 b x}}\right \},\left \{y(x)\to \frac {\sqrt {2 a^{5/2} b x^2-2 a^{5/2} c+4 a^3 b^2 x^3-4 a^3 b c x+a^2 x+4 \sqrt {a} b^2 c_1 x^2-4 \sqrt {a} b c c_1+2 b c_1 x}}{\sqrt {2} \sqrt {2 a^{3/2} b c_1+a^{7/2}+2 a^4 b x}}\right \}\right \}\] ✓ Maple : cpu = 0.295 (sec), leaf count = 97
\[\left \{y \left (x \right ) = \frac {\sqrt {\left (c_{1} x +1\right ) \left (\frac {x}{2}+\left (c_{1} x +1\right ) \left (b \,x^{2}-c \right ) \sqrt {a}\right ) a^{\frac {3}{2}}}}{\left (c_{1} x +1\right ) a^{\frac {3}{2}}}, y \left (x \right ) = -\frac {2 \sqrt {\left (c_{1} x +1\right ) \left (\frac {x}{2}+\left (c_{1} x +1\right ) \left (b \,x^{2}-c \right ) \sqrt {a}\right ) a^{\frac {3}{2}}}}{\left (2 c_{1} x +2\right ) a^{\frac {3}{2}}}\right \}\]