ODE No. 833

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

\[ y'(x)=\frac {x^4 \left (-\sqrt {x^2+y(x)^2}\right )+x^3 y(x) \sqrt {x^2+y(x)^2}+y(x)}{x} \] Mathematica : cpu = 0.141346 (sec), leaf count = 105

\[\left \{\left \{y(x)\to \frac {x \left (-2 e^{\sqrt {2} c_1+\frac {x^4}{2 \sqrt {2}}}+e^{2 \sqrt {2} c_1+\frac {x^4}{\sqrt {2}}}-1\right )}{2 e^{\sqrt {2} c_1+\frac {x^4}{2 \sqrt {2}}}+e^{2 \sqrt {2} c_1+\frac {x^4}{\sqrt {2}}}-1}\right \}\right \}\] Maple : cpu = 0.207 (sec), leaf count = 49

\[ \left \{ \ln \left ( 2\,{\frac {x \left ( \sqrt {2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,{x}^{2}}+y \left ( x \right ) +x \right ) }{y \left ( x \right ) -x}} \right ) +{\frac {\sqrt {2}{x}^{4}}{4}}-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \]