ODE No. 1640

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

\[ a y(x) y'(x)^2+b y(x)+y''(x)=0 \] Mathematica : cpu = 200.144 (sec), leaf count = 0 , could not solve

DSolve[b*y[x] + a*y[x]*Derivative[1][y][x]^2 + Derivative[2][y][x] == 0, y[x], x]

Maple : cpu = 0.217 (sec), leaf count = 70

\[ \left \{ \int ^{y \left ( x \right ) }\!{a{\frac {1}{\sqrt {a \left ( {{\rm e}^{-a{{\it \_a}}^{2}}}{\it \_C1}\,a-b \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{a{\frac {1}{\sqrt {a \left ( {{\rm e}^{-a{{\it \_a}}^{2}}}{\it \_C1}\,a-b \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]