Consider y'' = - sin(y)
find a conserved quantity for this equation
This looks an awful lot like a simplified version of a nonlinear pendulum equation
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!