1. Yesterday we discussed that F(t) = (r cos(c+t), -r sin(c+t)) and r(t) = (r sin(c+t),...

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1. Yesterday we discussed that F(t) = (r cos(c+t), -r sin(c+t)) and r(t) = (r sin(c+t), r cos(c+t)) both give the flow lines for the vector field F = (y,-x). I mentioned that the most general solution to the differential equation f" -f is the function Show that f(t) = R cos(t + c) + R2 sin(c2 +t), R1, R2, c1, c2 ER r(t) = (R cos(t + c) + R2 sin(c2 +t), -R sin(t + c) + R2 cos(c2 +t)) gives the same flow curves as the ones we found in class for the vector field F 2. Find the flow curves of the vector field F 3. Calculate (ay, x), where a R = (y, x) fds where C is the semicircle of radius 2 centered at the origin connecting (0,-2) to (0,2), and f(x, y) = xy. 1. Yesterday we discussed that F(t) = (r cos(c+t), -r sin(c+t)) and r(t) = (r sin(c+t), r cos(c+t)) both give the flow lines for the vector field F = (y,-x). I mentioned that the most general solution to the differential equation f" -f is the function Show that f(t) = R cos(t + c) + R2 sin(c2 +t), R1, R2, c1, c2 ER r(t) = (R cos(t + c) + R2 sin(c2 +t), -R sin(t + c) + R2 cos(c2 +t)) gives the same flow curves as the ones we found in class for the vector field F 2. Find the flow curves of the vector field F 3. Calculate (ay, x), where a R = (y, x) fds where C is the semicircle of radius 2 centered at the origin connecting (0,-2) to (0,2), and f(x, y) = xy.