2.409   ODE No. 409

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

\[ x y'(x)^2-2 y'(x)-y(x)=0 \] Mathematica : cpu = 30.8079 (sec), leaf count = 39

\[\text {Solve}\left [\left \{\text {K$\$$224706} x=\frac {y(\text {K$\$$224706})}{\text {K$\$$224706}}+2,y(x)=\frac {\text {K$\$$224706} \left (c_1 \text {K$\$$224706}-2 \text {K$\$$224706} \log (\text {K$\$$224706})-2\right )}{(\text {K$\$$224706}-1)^2}\right \},\{y(x),\text {K$\$$224706}\}\right ]\]

Maple : cpu = 0.055 (sec), leaf count = 63

\[ \left \{ y \left ( x \right ) =x{{\rm e}^{2\,{\it RootOf} \left ( -x{{\rm e}^{2\,{\it \_Z}}}+2\,x{{\rm e}^{{\it \_Z}}}+2\,{{\rm e}^{{\it \_Z}}}+{\it \_C1}-2\,{\it \_Z}-x \right ) }}-2\,{{\rm e}^{{\it RootOf} \left ( -x{{\rm e}^{2\,{\it \_Z}}}+2\,x{{\rm e}^{{\it \_Z}}}+2\,{{\rm e}^{{\it \_Z}}}+{\it \_C1}-2\,{\it \_Z}-x \right ) }} \right \} \]