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 = 0.101443 (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 = 1.013 (sec), leaf count = 137

\[\left \{y \left (x \right ) = -2, y \left (x \right ) = \frac {x^{2}-2 \sqrt {2}\, \sqrt {c_{1} x^{2}}}{c_{1}}, y \left (x \right ) = \frac {x^{2}+2 \sqrt {2}\, \sqrt {c_{1} x^{2}}}{c_{1}}, y \left (x \right ) = \frac {\left (x^{2}-8 c_{1}^{2}\right ) \left (-2 c_{1} \sqrt {2}+x \right ) x}{\left (8 c_{1}^{2}-4 c_{1} \sqrt {2}\, x +x^{2}\right ) c_{1}^{2}}, y \left (x \right ) = \frac {\left (x^{2}-8 c_{1}^{2}\right ) \left (2 c_{1} \sqrt {2}+x \right ) x}{\left (8 c_{1}^{2}+4 c_{1} \sqrt {2}\, x +x^{2}\right ) c_{1}^{2}}\right \}\]