1. The problem statement, all variables and given/known data Consider y'' = - sin(y) find a conserved quantity for this equation 2. Relevant equations This looks an awful lot like a simplified version of a nonlinear pendulum equation 3. The attempt at a solution For a conserved quantity I guessed: E = -cos(y) + y' because we need a y'' upon differentiating E and also we will need to cancel out the -sin(y) => dE/dt = sin(y)*y' + y'' => y'' = (dE/dt) - sin(y)*y' = -sin(y) => dE/dt = sin(y)*y' - sin(y) = sin(y)*(y'-1) and does not equal zero so E is not conserved. Please help me find a conserved quantity!