ODE No. 464

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

\[ y(x) y'(x)^2+2 x y'(x)-y(x)=0 \] Mathematica : cpu = 0.0653308 (sec), leaf count = 52

\[\left \{\left \{y(x)\to -e^{\frac {c_1}{2}} \sqrt {e^{c_1}-2 x}\right \},\left \{y(x)\to e^{\frac {c_1}{2}} \sqrt {e^{c_1}-2 x}\right \}\right \}\] Maple : cpu = 6.532 (sec), leaf count = 70

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