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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.