Sorry about this. I've solved this equation and I'm not quite getting what I am supposed to.
x''=-x can someone show me how to get the solution to this . Thanks
write as
x '' + x = 0
Assume solution of the form x = e^(rt)
Then plugging back into the original we obtain:
r^2e^(rt) + e^(rt) = 0
r^2 +1 = 0
This is the characteristic equation the solution is r = + i
The solutions are of the form e^(it) (you only need one of the complex solutions)
Using Euler's idenity e^(it) = cos(t) + i sin(t)
Then the real part: cos(t) and the imaginary part : sin(t) are the solutions
The general solution is x = Acos(t) + Bsin(t) which is easilyu verified to solve x '' + x = 0