Current Progress I am currently unable to proceed further, any help is welcomed. Looks forward to seeing different approaches to this differential equation.
$ {y}'' = A\sin(y) + B\cos(y) \\g(y)=A\sin{(y)}+B\cos{(y)} \\ {y}'' {y}'dx=g(y) {y}'dx \\ {y}'d{y}'=g(y)dy \\\frac{1}{2} {y}'^2=\int g(y)dy \\ {y}' = \pm \sqrt {2\int g(y)dy} \\ dx = \pm \frac{1}{\sqrt {2\int g(y)dy}} dy \\x=\pm\int\frac{1}{\sqrt {2\int g(y)dy}}dy \\x=\pm\int\frac{1}{\sqrt {2\int {(A\sin{(y)}+B\cos{(y)})}dy}} dy \\x=\pm\int\frac{1}{\sqrt {2B\sin{(y)}-2A\cos{(y)}+C}} dy $