8.17   ODE No. 1607

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

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

Mathematica: cpu = 0.108014 (sec), leaf count = 79 \[ \left \{\left \{y(x)\to -2 \text {am}\left (\frac {1}{2} \sqrt {\left (2 a+c_1\right ) \left (x+c_2\right ){}^2}|\frac {4 a}{2 a+c_1}\right )\right \},\left \{y(x)\to 2 \text {am}\left (\frac {1}{2} \sqrt {\left (2 a+c_1\right ) \left (x+c_2\right ){}^2}|\frac {4 a}{2 a+c_1}\right )\right \}\right \} \]

Maple: cpu = 0.078 (sec), leaf count = 49 \[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt {2\,a\cos \left ( {\it \_a} \right ) +{\it \_C1}}}}{d{\it \_a}}-x-{\it \_C2}=0, \int ^{y \left ( x \right ) }\!-{\frac {1}{\sqrt {2\,a\cos \left ( {\it \_a} \right ) +{\it \_C1}}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]