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 = 0.100942 (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 = 6.488 (sec), leaf count = 30

\[ \left \{ \ln \left ( \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}+y \left ( x \right ) \right ) -{\frac {{x}^{2}}{2}}-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \]