2.249   ODE No. 249

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

\[ y'(x) \left (a x y(x)+b x^n\right )+\alpha y(x)^3+\beta y(x)^2=0 \] Mathematica : cpu = 300.135 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 0.209 (sec), leaf count = 232

\[ \left \{ y \left ( x \right ) ={\beta \left ( {\it eval} \left ( {\it RootOf} \left ( -{x}^{1-n}{{\it \_Z}}^{{\frac {a \left ( n-1 \right ) }{\beta }}}{a}^{2}\beta \,n+{\it \_C1}\,{a}^{2}b{n}^{2}+{x}^{1-n}{{\it \_Z}}^{{\frac {a \left ( n-1 \right ) }{\beta }}}{a}^{2}\beta -{x}^{1-n}{{\it \_Z}}^{{\frac {a \left ( n-1 \right ) }{\beta }}}a{\beta }^{2}-{{\it \_Z}}^{{\frac {an-a+\beta }{\beta }}}\beta \,abn+{{\it \_Z}}^{{\frac {a \left ( n-1 \right ) }{\beta }}}a\alpha \,bn-2\,{\it \_C1}\,{a}^{2}bn+{\it \_C1}\,ab\beta \,n+{{\it \_Z}}^{{\frac {an-a+\beta }{\beta }}}\beta \,ab-{{\it \_Z}}^{{\frac {a \left ( n-1 \right ) }{\beta }}}a\alpha \,b+{{\it \_Z}}^{{\frac {a \left ( n-1 \right ) }{\beta }}}\alpha \,b\beta +{\it \_C1}\,{a}^{2}b-{\it \_C1}\,ab\beta \right ) , \left \{ {{\it \_Z}}^{{\frac {an-a+\beta }{\beta }}}={{\it \_Z}}^{{\frac {\beta +a \left ( n-1 \right ) }{\beta }}} \right \} \right ) \beta -\alpha \right ) ^{-1}} \right \} \]