ODE No. 1607

\[ a \sin (y(x))+y''(x)=0 \] Mathematica : cpu = 0.0799782 (sec), leaf count = 79

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

\[\left \{\left \{y(x)\to -2 \text {am}\left (\frac {1}{2} \sqrt {(2 a+c_1) (x+c_2){}^2}|\frac {4 a}{2 a+c_1}\right )\right \},\left \{y(x)\to 2 \text {am}\left (\frac {1}{2} \sqrt {(2 a+c_1) (x+c_2){}^2}|\frac {4 a}{2 a+c_1}\right )\right \}\right \}\] Maple : cpu = 0.163 (sec), leaf count = 49

dsolve(diff(diff(y(x),x),x)+a*sin(y(x))=0,y(x))
 

\[\int _{}^{y \left (x \right )}\frac {1}{\sqrt {2 a \cos \left (\textit {\_a} \right )+c_{1}}}d \textit {\_a} -x -c_{2} = 0\]