ODE No. 466

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

\[ y(x) y'(x)^2-2 x y'(x)+y(x)=0 \] Mathematica : cpu = 35.7116 (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 = 5.356 (sec), leaf count = 71

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