\[ y'(x)=\frac {1}{y(x)+\sqrt {x}} \] ✓ Mathematica : cpu = 0.0649803 (sec), leaf count = 445
\[\left \{\left \{y(x)\to -\sqrt {x}+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,1\right ]}\right \},\left \{y(x)\to -\sqrt {x}+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,2\right ]}\right \},\left \{y(x)\to -\sqrt {x}+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,3\right ]}\right \},\left \{y(x)\to -\sqrt {x}+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,4\right ]}\right \},\left \{y(x)\to -\sqrt {x}+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,5\right ]}\right \},\left \{y(x)\to -\sqrt {x}+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,6\right ]}\right \}\right \}\] ✓ Maple : cpu = 0.246 (sec), leaf count = 59
\[y \relax (x ) = \frac {\sqrt {x}\, \RootOf \left (\textit {\_Z}^{18} c_{1}-9 x \,\textit {\_Z}^{6}-6 \sqrt {x}\, \textit {\_Z}^{3}-1\right )^{3}+1}{\RootOf \left (\textit {\_Z}^{18} c_{1}-9 x \,\textit {\_Z}^{6}-6 \sqrt {x}\, \textit {\_Z}^{3}-1\right )^{3}}\]