Solve if y=5sinx+ 3cosx show that y"+ y =0 !?

1 Answer
Rhys
Feb 17, 2018

Answer below...

Explanation:

We must use our knowledge of trigonometric differentiation...

#d/(dx) ( sinx ) = cosx #

#d/(dx) ( cosx ) = -sinx #

If #y = 5sinx + 3 cosx #

#=> y' = 5cosx - 3sinx #

#=> y'' = (y')' = -5sinx - 3cosx #

#=> y'' + y = -5sinx - 3cosx + 5sinx + 3cosx = 0 #

#=> y'' + y = 0 #

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