2.833   ODE No. 833

\[ y'(x)=\frac {x^4 \left (-\sqrt {x^2+y(x)^2}\right )+x^3 y(x) \sqrt {x^2+y(x)^2}+y(x)}{x} \] Mathematica : cpu = 0.279044 (sec), leaf count = 221


\[\left \{\left \{y(x)\to \frac {x-2 \sqrt {x^2 \tanh ^2\left (\frac {1}{4} \left (-\sqrt {2} x^4-4 \sqrt {2} c_1\right )\right )-x^2 \tanh ^4\left (\frac {1}{4} \left (-\sqrt {2} x^4-4 \sqrt {2} c_1\right )\right )}}{-1+2 \tanh ^2\left (\frac {1}{4} \left (-\sqrt {2} x^4-4 \sqrt {2} c_1\right )\right )}\right \},\left \{y(x)\to \frac {x+2 \sqrt {x^2 \tanh ^2\left (\frac {1}{4} \left (-\sqrt {2} x^4-4 \sqrt {2} c_1\right )\right )-x^2 \tanh ^4\left (\frac {1}{4} \left (-\sqrt {2} x^4-4 \sqrt {2} c_1\right )\right )}}{-1+2 \tanh ^2\left (\frac {1}{4} \left (-\sqrt {2} x^4-4 \sqrt {2} c_1\right )\right )}\right \}\right \}\] Maple : cpu = 0.153 (sec), leaf count = 49


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