i cant see how they got X and Y expressions

V_x is the derivative of X(t) by t

'A' and phi are needed to be found

but when i dont know how to innpur the initial condition to find A_x and A_y

because when we integrate x' expression bot sides i get

x(t)-x(0)=[A_x*cos(wt+phi)]/w - [A_x*cos(0+phi)]/w

so i cant put 'b' instead of x(0) but it doesnt give me A_x parameter value