Hey
I am not sure if this is the right section to put this in as this is my first post...
I am trying to calculate the streamline of u=(ay, -ax, 0)
I know i need to solve this set of differential equations:
dx/ds = ay, dy/ds= -ax , dz/ds=0

I am supposed to get a solution of:
x = yo sin (as) + xo cos (as)
y = yo cos (as) - xo sin (as)
z = zo

where xo, yo, zo are the intial conditions.
I don't understand where the sin and cos have come from.
Thank you for any help

trick
taking the derivative of dx/ds=ay again. now i get, d^2x/ds^2=a dy/ds=-a^2x
since i already know dy/ds=-ax(as u have noted) .....now that is an shm equation and obviously the solution will be in sin and cos.
same thing for dy/ds=-ax, take derivative wrt s again on both sides and substitute.
and z will be constant because derivative zero.
hope that helps.