2.115   ODE No. 115

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

\[ -x (y(x)-x) \sqrt {x^2+y(x)^2}+x y'(x)-y(x)=0 \] Mathematica : cpu = 0.124501 (sec), leaf count = 99

\[\left \{\left \{y(x)\to \frac {x \left (-2 e^{\sqrt {2} c_1+\frac {x^2}{\sqrt {2}}}+e^{2 \sqrt {2} c_1+\sqrt {2} x^2}-1\right )}{2 e^{\sqrt {2} c_1+\frac {x^2}{\sqrt {2}}}+e^{2 \sqrt {2} c_1+\sqrt {2} x^2}-1}\right \}\right \}\]

Maple : cpu = 0.227 (sec), leaf count = 49

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