3.464   ODE No. 464

\[ \boxed { y \left ( x \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+2\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.061008 (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 = 0.983 (sec), leaf count = 71 \[ \left \{ y \left ( x \right ) =\sqrt {{{\it \_C1}}^{2}-2\,{\it \_C1}\,x} ,y \left ( x \right ) =\sqrt {{{\it \_C1}}^{2}+2\,{\it \_C1}\,x},y \left ( x \right ) =-ix,y \left ( x \right ) =ix,y \left ( x \right ) =- \sqrt {{{\it \_C1}}^{2}-2\,{\it \_C1}\,x},y \left ( x \right ) =-\sqrt { {{\it \_C1}}^{2}+2\,{\it \_C1}\,x} \right \} \]