Posted by Claire on Friday, March 25, 2011 at 3:18pm.
the hard part is to integrate the cos^2x
we know that cos 2x = 2cos^2x - 1
so replace the 2cos^2x with cos2x + 1
then
dy/dx = 1+2cos^2x
= 1 + cos2x + 1 = 2 + cos2x
then y = 2x + (1/2)sin2x + c
given: when x=0, y = 1
1 = 0 + sin0 + c
c = 1
y = 2x + (1/2)sin2x + 1
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