2.621   ODE No. 621

\[ y'(x)=\frac {1}{y(x)+\sqrt {x}} \]

✓ Mathematica : cpu = 0.0515312 (sec), leaf count = 445

DSolve[Derivative[1][y][x] == (Sqrt[x] + y[x])^(-1),y[x],x]
 

\[\left \{\left \{y(x)\to -\sqrt {x}+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,1\right ]}\right \},\left \{y(x)\to -\sqrt {x}+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,2\right ]}\right \},\left \{y(x)\to -\sqrt {x}+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,3\right ]}\right \},\left \{y(x)\to -\sqrt {x}+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,4\right ]}\right \},\left \{y(x)\to -\sqrt {x}+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,5\right ]}\right \},\left \{y(x)\to -\sqrt {x}+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^3+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^2+8 \text {$\#$1}^3 x^{3/2}+9 \text {$\#$1}^2 x-6 \text {$\#$1} \sqrt {x}+1\& ,6\right ]}\right \}\right \}\]

✓ Maple : cpu = 0.354 (sec), leaf count = 59

dsolve(diff(y(x),x) = 1/(y(x)+x^(1/2)),y(x))
 

\[y \left (x \right ) = \frac {\sqrt {x}\, \operatorname {RootOf}\left (\textit {\_Z}^{18} c_{1} -9 x \,\textit {\_Z}^{6}-6 \sqrt {x}\, \textit {\_Z}^{3}-1\right )^{3}+1}{\operatorname {RootOf}\left (\textit {\_Z}^{18} c_{1} -9 x \,\textit {\_Z}^{6}-6 \sqrt {x}\, \textit {\_Z}^{3}-1\right )^{3}}\]