\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) = \left ( y \left ( x \right ) +\sqrt {x} \right ) ^{-1}=0} \]
Mathematica: cpu = 0.098513 (sec), leaf count = 445 \[ \left \{\left \{y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 e^{12 c_1}+16 x^3\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,1\right ]}-\sqrt {x}\right \},\left \{y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 e^{12 c_1}+16 x^3\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,2\right ]}-\sqrt {x}\right \},\left \{y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 e^{12 c_1}+16 x^3\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,3\right ]}-\sqrt {x}\right \},\left \{y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 e^{12 c_1}+16 x^3\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,4\right ]}-\sqrt {x}\right \},\left \{y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 e^{12 c_1}+16 x^3\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,5\right ]}-\sqrt {x}\right \},\left \{y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 e^{12 c_1}+16 x^3\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,6\right ]}-\sqrt {x}\right \}\right \} \]
Maple: cpu = 0.234 (sec), leaf count = 59 \[ \left \{ y \left ( x \right ) ={1 \left ( \sqrt {x} \left ( {\it RootOf} \left ( {{\it \_Z}}^{18}{\it \_C1}-9\,x{{\it \_Z}}^{6}-6\,\sqrt {x}{{ \it \_Z}}^{3}-1 \right ) \right ) ^{3}+1 \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{18}{\it \_C1}-9\,x{{\it \_Z}}^{6}-6\,\sqrt {x}{{ \it \_Z}}^{3}-1 \right ) \right ) ^{-3}} \right \} \]