2.1638   ODE No. 1638

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

\[ a y'(x)^2+b \sin (y(x))+y''(x)=0 \] Mathematica : cpu = 100.099 (sec), leaf count = 0 , could not solve

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

Maple : cpu = 0.189 (sec), leaf count = 126

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