2.410   ODE No. 410

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

\[ x y'(x)^2+4 y'(x)-2 y(x)=0 \] Mathematica : cpu = 31.0387 (sec), leaf count = 40

\[\text {Solve}\left [\left \{\text {K$\$$225417} x+4=\frac {2 y(\text {K$\$$225417})}{\text {K$\$$225417}},y(x)=\frac {\text {K$\$$225417} \left (c_1 \text {K$\$$225417}+4 \text {K$\$$225417} \log (\text {K$\$$225417})+8\right )}{(\text {K$\$$225417}-2)^2}\right \},\{y(x),\text {K$\$$225417}\}\right ]\]

Maple : cpu = 0.056 (sec), leaf count = 64

\[ \left \{ y \left ( x \right ) ={\frac {x{{\rm e}^{2\,{\it RootOf} \left ( -x{{\rm e}^{2\,{\it \_Z}}}+4\,x{{\rm e}^{{\it \_Z}}}-4\,{{\rm e}^{{\it \_Z}}}+{\it \_C1}+8\,{\it \_Z}-4\,x \right ) }}}{2}}+2\,{{\rm e}^{{\it RootOf} \left ( -x{{\rm e}^{2\,{\it \_Z}}}+4\,x{{\rm e}^{{\it \_Z}}}-4\,{{\rm e}^{{\it \_Z}}}+{\it \_C1}+8\,{\it \_Z}-4\,x \right ) }} \right \} \]