\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) ={\frac {150\,{x}^{3}+125\,\sqrt {x}+125+125\, \left( y \left( x \right)  \right) ^{2}-100\,{x}^{3}y \left( x \right) -500\,y \left( x \right) \sqrt {x}+20\,{x}^{6}+200\,{x}^{7/2}+500\,x+125\, \left( y \left( x \right)  \right) ^{3}-150\,{x}^{3} \left( y \left( x \right)  \right) ^{2}-750\, \left( y \left( x \right)  \right) ^{2}\sqrt {x}+60\,y \left( x \right) {x}^{6}+600\,y \left( x \right) {x}^{7/2}+1500\,xy \left( x \right) -8\,{x}^{9}-120\,{x}^{13/2}-600\,{x}^{4}-1000\,{x}^{3/2}}{125\,x}}=0}
\]