SOLUTION: Let S be the set of all solutions to the differential equation y^n = -y. THe functions y = sinx and y = cosx are solutions and are linearly independent (becasue if asinx+bcosx=0 a
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Question 839173: Let S be the set of all solutions to the differential equation y^n = -y. THe functions y = sinx and y = cosx are solutions and are linearly independent (becasue if asinx+bcosx=0 all x then a=b=0). In fact, one can show that B = {sinx, cosx} is a basis of S.
(a) Show that y = sin(x+(pi/3)) is an element of S.
(b) Find the coordinate vector [sin(x+(pi/3)]B Hint: use a trig sum formula
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
(a)  = \sin x \cos \frac{\pi}{3} + \cos x \sin \frac{\pi}{3} = \frac{1}{2} \sin x + \frac{\sqrt{3}}{2} \cos x)
, which is an element of S.
(b) Just did that in part (a).
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