I got this
DSolve[k1*y''[t] == k2*y'[t] - k3*Sin[y[t]], y[t], t]
But when I try to run it there is a error: "Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information."
I'll like to if some one knows how to solve it, k1,k2,k3 are constants
Reduce[k1*y''[t] == k2*y'[t] - k3*Sin[y[t]], y[t]]
and carefully match the '()` and the precedence of||
versus&&
and see if you can make out two or three separate differential equations to try if all the conditions are satisfied. If that works then carefully check by substituting the solutions back into the original to see if they hold. $\endgroup$ – Bill Nov 28 '18 at 2:55