Need Help Solving Initial Value Differential Equation

[swooshfactory]

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.

 

[Dick]

sin(0)=0 and e^(0)=1 not e.