2.829   ODE No. 829

\[ y'(x)=\frac {x^6 \sqrt {4 x^2 y(x)+1}+x^5 \sqrt {4 x^2 y(x)+1}+x^3 \sqrt {4 x^2 y(x)+1}+\frac {1}{2}}{x^3} \] Mathematica : cpu = 0.442082 (sec), leaf count = 74


\[\left \{\left \{y(x)\to \frac {16 x^{12}+40 x^{11}+25 x^{10}+80 x^9+100 x^8-160 c_1 x^7+100 x^6-200 c_1 x^6-400 c_1 x^4+400 c_1{}^2 x^2-100}{400 x^2}\right \}\right \}\] Maple : cpu = 0.372 (sec), leaf count = 34


\[c_{1}-\frac {\sqrt {4 x^{2} y \relax (x )+1}}{x}+x^{2}+\frac {x^{4}}{2}+\frac {2 x^{5}}{5} = 0\]