dx/dt=ay and dy/dt=bx where x and y are function of t [x(t) and y(t)] and a and b are constant. 1) show what x and y satisfy the equation for a hyperbola: y^2-(b/a)*x^2=(y_0)^2-(b/a)*(x_0)^2 2) suppose at some time t_s, the point (x(t_s),y(t_s)) lies on the upper branch of hyperbola, show that: y(t_s)>sqrt(b/a)*x(t_s) I dun know whether i am doing it right. First, in integrate both equations, dx/dt=ay >>> x/y+C_1=at+C_2 >>> x/y+C_5=at dy/dt=bx >>> y/x+C_3=bt+C_4 >>> y/x+C_6=bt then I say t = 0 and so x/y+C_5=at >>> C_5=-x_0/y_0 y/x+C_6=bt >>> C_6=-y_0/x_0 then i say this happens only when C_5 and C_6 are 0 then going back to x/y+C_5=at >>> x/y=at y/x+C_6=bt >>> y/x=bt and isolating t to yield y^2-(b/a)*x^2=0 and when t=0 y_0^2-(b/a)*x_0^2=0 so y^2-(b/a)*x^2=y_0^2-(b/a)*x_0^2 am i right about it? and can somebody give me some hints to deal with the second problem? thank you.