2.1615   ODE No. 1615

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

\[ -\frac {2 (n+1) (n+2) y(x) \left (y(x)^{\frac {n}{n+1}}-1\right )}{n^2}-\frac {(3 n+4) y'(x)}{n}+y''(x)=0 \] Mathematica : cpu = 112.949 (sec), leaf count = 0 , could not solve

DSolve[(-2*(1 + n)*(2 + n)*y[x]*(-1 + y[x]^(n/(1 + n))))/n^2 - ((4 + 3*n)*Derivative[1][y][x])/n + Derivative[2][y][x] == 0, y[x], x]

Maple : cpu = 4.551 (sec), leaf count = 116

\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) -{\frac {1}{{n}^{2}} \left ( 2\,{{\it \_a}}^{{\frac {n}{n+1}}}{\it \_a}\,{n}^{2}+6\,{{\it \_a}}^{{\frac {n}{n+1}}}{\it \_a}\,n+3\,{\it \_b} \left ( {\it \_a} \right ) {n}^{2}-2\,{\it \_a}\,{n}^{2}+4\,{{\it \_a}}^{{\frac {n}{n+1}}}{\it \_a}+4\,{\it \_b} \left ( {\it \_a} \right ) n-6\,{\it \_a}\,n-4\,{\it \_a} \right ) }=0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \]