2.1669   ODE No. 1669

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

\[ -x^2 y'(x)^2+x y''(x)+2 y'(x)+y(x)^2=0 \] Mathematica : cpu = 125.481 (sec), leaf count = 74

\[\text {Solve}\left [\int _1^x -\frac {c_1 e^{K[2]}+K[2]+1}{c_1 e^{K[2]} K[2]+2 K[2]^2+K[2]} \, dK[2]+c_2=\int _1^{y(x)} -\frac {x}{c_1 e^{x K[1]}+2 x K[1]+1} \, dK[1],y(x)\right ]\]

Maple : cpu = 0.119 (sec), leaf count = 32

\[ \left \{ y \left ( x \right ) ={\frac {1}{x}{\it RootOf} \left ( -\ln \left ( x \right ) +{\it \_C2}+\int ^{{\it \_Z}}\!- \left ( {{\rm e}^{{\it \_f}}}{\it \_C1}-2\,{\it \_f}-1 \right ) ^{-1}{d{\it \_f}} \right ) } \right \} \]