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 = 100.119 (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 = 0.226 (sec), leaf count = 115

\[ \left \{ \int ^{y \left ( x \right ) }\!{(-4\,{a}^{2}-1){\frac {1}{\sqrt {16\, \left ( {a}^{2}+1/4 \right ) ^{2}{\it \_C1}\,{{\rm e}^{-2\,a{\it \_a}}}-16\, \left ( {a}^{2}+1/4 \right ) \left ( a\sin \left ( {\it \_a} \right ) -1/2\,\cos \left ( {\it \_a} \right ) \right ) b}}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!{(4\,{a}^{2}+1){\frac {1}{\sqrt {16\, \left ( {a}^{2}+1/4 \right ) ^{2}{\it \_C1}\,{{\rm e}^{-2\,a{\it \_a}}}-16\, \left ( {a}^{2}+1/4 \right ) \left ( a\sin \left ( {\it \_a} \right ) -1/2\,\cos \left ( {\it \_a} \right ) \right ) b}}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]