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## Homework Statement

dy/dx + y*cos(x) = 3*cos(x) . Find the particular solution of the differential equation dy/dx + y*cos(x) = 3*cos(x) satisfying the initial condition y(0)=5.

y(x) = ________________________

## Homework Equations

## The Attempt at a Solution

I thought I had done it the right way, but my computer based homework system disagreed.

Heres my work:

p(t)=cos(x)

g(t)=3cos(x)

m: mu

m(t)=exp [int] cos(x)dx

m(t)= e^sin(x)

then,

e^sinx(y)= [int]3cosx(e^sinx)dx

[int]3cosx(e^sinx)dx= 3(e^sinx)+C

then to solve for y,

y= 3(e^sin(x)+C)/(e^sin(x))

using the intial value to solve for C, [[the initial value was y(0)=5]]

5=3(e+C)/e

5e=3e + C<<<right here is it C or 3c?>>

c=2e

and plugging it back into the y-equation, I get y=(3(e^sinx)+2e)/(e^sinx)

Where have I gone wrong? My homework system says this is wrong... Any help would be greatly appreciated. Thank you for looking.