3.466   ODE No. 466

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

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

Mathematica: cpu = 0.248532 (sec), leaf count = 145 \[ \left \{\left \{y(x)\to -\sqrt {-2 x \sinh \left (c_1\right )-2 x \cosh \left (c_1\right )-\sinh \left (2 c_1\right )-\cosh \left (2 c_1\right )}\right \},\left \{y(x)\to \sqrt {-2 x \sinh \left (c_1\right )-2 x \cosh \left (c_1\right )-\sinh \left (2 c_1\right )-\cosh \left (2 c_1\right )}\right \},\left \{y(x)\to -\sqrt {2 x \sinh \left (c_1\right )+2 x \cosh \left (c_1\right )-\sinh \left (2 c_1\right )-\cosh \left (2 c_1\right )}\right \},\left \{y(x)\to \sqrt {2 x \sinh \left (c_1\right )+2 x \cosh \left (c_1\right )-\sinh \left (2 c_1\right )-\cosh \left (2 c_1\right )}\right \}\right \} \]

Maple: cpu = 0.811 (sec), leaf count = 71 \[ \left \{ y \left ( x \right ) =x,y \left ( x \right ) =\sqrt {{{\it \_C1}} ^{2}-2\,ix{\it \_C1}},y \left ( x \right ) =\sqrt {{{\it \_C1}}^{2}+2\,i x{\it \_C1}},y \left ( x \right ) =-x,y \left ( x \right ) =-\sqrt {{{\it \_C1}}^{2}-2\,ix{\it \_C1}},y \left ( x \right ) =-\sqrt {{{\it \_C1}}^{ 2}+2\,ix{\it \_C1}} \right \} \]