#### 2.621   ODE No. 621

$y'(x)=\frac {1}{y(x)+\sqrt {x}}$ Mathematica : cpu = 0.0561221 (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 = 0.237 (sec), leaf count = 59

$\left \{ y \left ( x \right ) ={1 \left ( \sqrt {x} \left ( {\it RootOf} \left ( {{\it \_Z}}^{18}{\it \_C1}-9\,x{{\it \_Z}}^{6}-6\,\sqrt {x}{{\it \_Z}}^{3}-1 \right ) \right ) ^{3}+1 \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{18}{\it \_C1}-9\,x{{\it \_Z}}^{6}-6\,\sqrt {x}{{\it \_Z}}^{3}-1 \right ) \right ) ^{-3}} \right \}$