2.472   ODE No. 472

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

\[ (y(x)+x) y'(x)^2+2 x y'(x)-y(x)=0 \] Mathematica : cpu = 0.184077 (sec), leaf count = 121

\[\left \{\left \{y(x)\to -\frac {2}{3} \sqrt {e^{c_1} \left (e^{c_1}-3 x\right )}-\frac {e^{c_1}}{3}\right \},\left \{y(x)\to \frac {2}{3} \sqrt {e^{c_1} \left (e^{c_1}-3 x\right )}-\frac {e^{c_1}}{3}\right \},\left \{y(x)\to e^{c_1}-2 \sqrt {e^{c_1} \left (e^{c_1}+x\right )}\right \},\left \{y(x)\to 2 \sqrt {e^{c_1} \left (e^{c_1}+x\right )}+e^{c_1}\right \}\right \}\]

Maple : cpu = 0.475 (sec), leaf count = 121

\[ \left \{ \ln \left ( x \right ) -{\it Artanh} \left ( {\frac {y \left ( x \right ) +2\,x}{2\,x}{\frac {1}{\sqrt {{\frac { \left ( y \left ( x \right ) \right ) ^{2}+xy \left ( x \right ) +{x}^{2}}{{x}^{2}}}}}}} \right ) +\ln \left ( {\frac {y \left ( x \right ) }{x}} \right ) -{\it \_C1}=0,\ln \left ( x \right ) +{\it Artanh} \left ( {\frac {y \left ( x \right ) +2\,x}{2\,x}{\frac {1}{\sqrt {{\frac { \left ( y \left ( x \right ) \right ) ^{2}+xy \left ( x \right ) +{x}^{2}}{{x}^{2}}}}}}} \right ) +\ln \left ( {\frac {y \left ( x \right ) }{x}} \right ) -{\it \_C1}=0,y \left ( x \right ) =-{\frac { \left ( 1+i\sqrt {3} \right ) x}{2}},y \left ( x \right ) ={\frac { \left ( i\sqrt {3}-1 \right ) x}{2}} \right \} \]