ODE No. 827

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

\[ y'(x)=\frac {x^2 y(x) \sqrt {x^2+y(x)^2}+x^3 \left (-\sqrt {x^2+y(x)^2}\right )+y(x)}{x} \] Mathematica : cpu = 0.142973 (sec), leaf count = 111

\[\left \{\left \{y(x)\to \frac {x \left (-2 e^{\sqrt {2} c_1+\frac {\sqrt {2} x^3}{3}}+e^{2 \sqrt {2} c_1+\frac {2 \sqrt {2} x^3}{3}}-1\right )}{2 e^{\sqrt {2} c_1+\frac {\sqrt {2} x^3}{3}}+e^{2 \sqrt {2} c_1+\frac {2 \sqrt {2} x^3}{3}}-1}\right \}\right \}\] Maple : cpu = 0.261 (sec), leaf count = 49

\[ \left \{ \ln \left ( 2\,{\frac {x \left ( \sqrt {2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,{x}^{2}}+y \left ( x \right ) +x \right ) }{y \left ( x \right ) -x}} \right ) +{\frac {\sqrt {2}{x}^{3}}{3}}-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \]