\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {b{x}^{3}+{c}^{2}\sqrt {a}-2\,cb{x}^{2}\sqrt {a}+2\,c \left ( y \left ( x \right ) \right ) ^{2}{a}^{3/2}+{b}^{2}{x}^{4}\sqrt {a}-2\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{3/2}b{x}^{2}+{a}^{5/2} \left ( y \left ( x \right ) \right ) ^{4}}{a{x}^{2}y \left ( x \right ) }}=0} \]
Mathematica: cpu = 1.255659 (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 = 0.234 (sec), leaf count = 97 \[ \left \{ y \left ( x \right ) ={\frac {1}{x{\it \_C1}+1}\sqrt { \left ( \left ( x{\it \_C1}+1 \right ) \left ( b{x}^{2}-c \right ) \sqrt {a}+{ \frac {x}{2}} \right ) \left ( x{\it \_C1}+1 \right ) {a}^{{\frac {3}{2} }}}{a}^{-{\frac {3}{2}}}},y \left ( x \right ) =-2\,{\frac {\sqrt { \left ( \left ( x{\it \_C1}+1 \right ) \left ( b{x}^{2}-c \right ) \sqrt {a}+x/2 \right ) \left ( x{\it \_C1}+1 \right ) {a}^{3/2}}}{{a}^{3 /2} \left ( 2\,x{\it \_C1}+2 \right ) }} \right \} \]