2.684   ODE No. 684

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ y'(x)=\frac {x^2 \sqrt {x^2+y(x)^2}+y(x)}{x} \] Mathematica : cpu = 0.137231 (sec), leaf count = 20

\[\left \{\left \{y(x)\to x \sinh \left (\frac {1}{2} \left (x^2+2 c_1\right )\right )\right \}\right \}\] Maple : cpu = 4.142 (sec), leaf count = 30

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