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y''+y=2sect + 3 (-pi/2 < t < pi/2)

using variation of parameters.

I just needed a check to make sure my answer was correct.

r^2+1 = 0

r= -i

r= i

y1= cost

y2= sint

g(t)= 2sect+ 3

y(t) = c1cost + c2sint + Y(t)

Y(t) = u1y1 + u2y2

u1 = -(integal) (y2*g(t))/W in which W = 1

= -(int) sint(2sect+ 3)

= -(int) sint(2/cost+3)

= -(2 (int) tant + 3 (int) sint)

is this correct, where do i go from here

u2= (integral) y1*g(t)/ W

= (int) cost(2sect + 3)/ W

= (int) (2*(cost/cost) + 3cost)

= (int) 2 + (int)3 cost

= 2+3(sint)

is this correct

and then I plug these back into the Y(t) eq and add this to y(t)?