I am struggling to find the solution to the differential equation:
$\dot x(t)+x(-t)=0; x(0)=0$
Basically, I can't figure out how the reflection in $t$ affects the solution, and from there how to include the initial condition. I know the function that solves this must cross the origin with no slope (so you can't just shift over a trig function), and I would assume it is related to the exponential function, since the derivative will need to cancel out the reflection of the original function. I would really appreciate it if someone could explain how I can approach this problem (preferably without giving the solution). Thanks!