How does the shooting method work if $x(t_0)$ and $\dot{x}(t_1)$ are given?

Question

we're supposed to write a script that solves the ODE $\ddot{x}(t) = a_1x(t)+a_2\dot{x}(t)$ with a given interval $[t_0,t_1]$ and initial values $x(t_0)$ and $\dot{x}(t_1)$ using Newton's method and Runge-Kutta. I've understood how the shooting method can be used to approximate the solution for given $x(t_0)$ and $x(t_1)$, but I'm stuck trying to find out how we can go on about this type of problem. Any help would be appreciated!