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 = 1.8505 (sec), leaf count = 49

\[\left \{\left \{y(x)\to 0^{\frac {1}{-a-1}}\right \},\left \{y(x)\to 2^{\frac {1}{-2 a-3}} \left (\frac {b}{(2 a+3) c_1}\right ){}^{\frac {1}{-2 a-3}}\right \}\right \}\] Maple : cpu = 0.398 (sec), leaf count = 107

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