2.1717   ODE No. 1717

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

\[ a y'(x)^2+b y(x)^3+y(x) y''(x)=0 \] Mathematica : cpu = 50.9877 (sec), leaf count = 0 , could not solve

DSolve[b*y[x]^3 + a*Derivative[1][y][x]^2 + y[x]*Derivative[2][y][x] == 0, y[x], x]

Maple : cpu = 1.371 (sec), leaf count = 107

\[ \left \{ \int ^{y \left ( x \right ) }\!{{{\it \_a}}^{2\,a} \left ( 2\,a+3 \right ) {\frac {1}{\sqrt {-{{\it \_a}}^{2\,a} \left ( 2\,a+3 \right ) \left ( 2\,{{\it \_a}}^{2\,a+3}b-{\it \_C1} \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!{ \left ( -2\,a-3 \right ) {{\it \_a}}^{2\,a}{\frac {1}{\sqrt {-{{\it \_a}}^{2\,a} \left ( 2\,a+3 \right ) \left ( 2\,{{\it \_a}}^{2\,a+3}b-{\it \_C1} \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]