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## Homework Statement

Find the gerneral solution of the differential equation below:

dy/dt=(-y/t)+2

## Homework Equations

none

## The Attempt at a Solution

my solution by using integrating factor:

1.find the homogenous solution first

dy/y = -1/t dt

you get ln(y) = -ln(t) when integrating both side.

you get y = -t

2. find gerenal soultion:

u(t) = 1/y(homogenous)

so in this case u(t) =1/-t, b(t) = 2

now apply integrating method:

(u(t)y(t))' = u(t)b(t)

(y(t)/-t)' = 2/-t

taking integral of both side we get

y(t)/-t = -2ln(t)+c = -ln(t^2)+c

then Y(t) = -t(-ln(t^2)+c) = -tln(t^2)+-tc

we get y(t) = -tln(t^2)+-tc for general solution.

but the book answer is y(t) = t+c/t

so did I do anything wrong, I dont really find anything wrong myself.