Convert to standard form ODE system y' = f(t, y):
(t^2)y'' + sin(y') + 2y − 1 = 0
the goal is to reduce the equation above to be a first order ode.
Hmm...
I know that if you make the substitutions $\displaystyle u_1=y$ and $\displaystyle u_2=\dot{y}$, you will see that $\displaystyle \dot{u_1}=\dot{y}=u_2$ and $\displaystyle \dot{u_2}=\ddot{y}$
Thus, you get the first order system
$\displaystyle \left\{\begin{array}{lcl}
\dot{u_1}=u_2\\ \dot{u_2}=t^{-2}-2u_1t^{-2}-t^{-2}\sin\left(u_2\right)\end{array}\right.$
Does this make sense?