2.466   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 = 0.243837 (sec), leaf count = 119

\[\left \{\left \{y(x)\to -\sqrt {-\left (\sinh \left (c_1\right )+\cosh \left (c_1\right )\right ) \left (\sinh \left (c_1\right )+\cosh \left (c_1\right )+2 x\right )}\right \},\left \{y(x)\to \sqrt {-\left (\sinh \left (c_1\right )+\cosh \left (c_1\right )\right ) \left (\sinh \left (c_1\right )+\cosh \left (c_1\right )+2 x\right )}\right \},\left \{y(x)\to -\sqrt {\left (\sinh \left (c_1\right )+\cosh \left (c_1\right )\right ) \left (-\sinh \left (c_1\right )-\cosh \left (c_1\right )+2 x\right )}\right \},\left \{y(x)\to \sqrt {\left (\sinh \left (c_1\right )+\cosh \left (c_1\right )\right ) \left (-\sinh \left (c_1\right )-\cosh \left (c_1\right )+2 x\right )}\right \}\right \}\]

Maple : cpu = 0.391 (sec), leaf count = 71

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