8.48   ODE No. 1638

\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +a \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+b\sin \left ( y \left ( x \right ) \right ) =0} \]

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

Mathematica: cpu = 100.155218 (sec), leaf count = 24 \[ \text {DSolve}\left [a y'(x)^2+b \sin (y(x))+y''(x)=0,y(x),x\right ] \]

Maple: cpu = 0.125 (sec), leaf count = 126 \[ \left \{ \int ^{y \left ( x \right ) }\!{(4\,{a}^{2}+1){\frac {1}{\sqrt { \left ( 4\,{a}^{2}+1 \right ) \left ( 4\,{{\rm e}^{-2\,a{\it \_a}}}{ \it \_C1}\,{a}^{2}-4\,\sin \left ( {\it \_a} \right ) ab+2\,b\cos \left ( {\it \_a} \right ) +{{\rm e}^{-2\,a{\it \_a}}}{\it \_C1} \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\! -{(4\,{a}^{2}+1){\frac {1}{\sqrt { \left ( 4\,{a}^{2}+1 \right ) \left ( 4\,{{\rm e}^{-2\,a{\it \_a}}}{\it \_C1}\,{a}^{2}-4\,\sin \left ( {\it \_a} \right ) ab+2\,b\cos \left ( {\it \_a} \right ) +{ {\rm e}^{-2\,a{\it \_a}}}{\it \_C1} \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]