2.441   ODE No. 441

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

\[ x^2 y'(x)^2-4 x (y(x)+2) y'(x)+4 y(x) (y(x)+2)=0 \] Mathematica : cpu = 0.0814584 (sec), leaf count = 65

\[\left \{\left \{y(x)\to -e^{-c_1} x \left (-x+2 \sqrt {2} e^{\frac {c_1}{2}}\right )\right \},\left \{y(x)\to e^{\frac {c_1}{2}} x \left (-2 \sqrt {2}+e^{\frac {c_1}{2}} x\right )\right \}\right \}\] Maple : cpu = 4.88 (sec), leaf count = 83

\[ \left \{ y \left ( x \right ) =-2,y \left ( x \right ) ={\frac {1}{{\it \_C1}} \left ( {x}^{2}-2\,\sqrt {2}\sqrt {{\it \_C1}\,{x}^{2}} \right ) },y \left ( x \right ) ={\frac {1}{{\it \_C1}} \left ( 2\,\sqrt {2}\sqrt {{\it \_C1}\,{x}^{2}}+{x}^{2} \right ) },y \left ( x \right ) ={\frac {x \left ( -2\,\sqrt {2}{\it \_C1}+x \right ) }{{{\it \_C1}}^{2}}},y \left ( x \right ) ={\frac {x \left ( 2\,\sqrt {2}{\it \_C1}+x \right ) }{{{\it \_C1}}^{2}}} \right \} \]