2.872   ODE No. 872

\[ y'(x)=\frac {14 x^{7/2}+\frac {12 x^6}{5}-6 x^3 y(x)-6 x^3-5 \sqrt {x} y(x)+10 x-5 \sqrt {x}-5}{x \left (2 x^3-5 y(x)+10 \sqrt {x}-5\right )} \] Mathematica : cpu = 0.060433 (sec), leaf count = 215


\[\left \{\left \{y(x)\to \frac {1}{5} \left (2 x^3+10 \sqrt {x}-5\right )-\frac {\sqrt {-x \left (2 x^3+10 \sqrt {x}-5\right )^2-50 x \left (-\frac {4 x^{7/2}}{5}-\frac {2 x^6}{25}+\frac {2 x^3}{5}-2 x+2 \sqrt {x}+\log (x)\right )-25 c_1 x}}{5 \sqrt {-\frac {1}{x}} x}\right \},\left \{y(x)\to \frac {1}{5} \left (2 x^3+10 \sqrt {x}-5\right )+\frac {\sqrt {-x \left (2 x^3+10 \sqrt {x}-5\right )^2-50 x \left (-\frac {4 x^{7/2}}{5}-\frac {2 x^6}{25}+\frac {2 x^3}{5}-2 x+2 \sqrt {x}+\log (x)\right )-25 c_1 x}}{5 \sqrt {-\frac {1}{x}} x}\right \}\right \}\] Maple : cpu = 0.064 (sec), leaf count = 49


\[y \relax (x ) = \frac {2 x^{3}}{5}+2 \sqrt {x}-\sqrt {c_{1}+2 \ln \relax (x )}-1\]