- #1
Mr Davis 97
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- 44
Homework Statement
##\displaystyle (x+3)\frac{dy}{dx} = y - 2##, where x is not 3 and y is not 2.
Homework Equations
The Attempt at a Solution
##\displaystyle (x+3)\frac{dy}{dx} = y - 2##
##\displaystyle \frac{dy}{y-2} = \frac{dx}{x+3}##
##\displaystyle \int \frac{dy}{y-2} = \int \frac{dx}{x+3}##
##\ln|y-2| = \ln|x+3| + c##
##\displaystyle |y-2| = e^{\ln |x+3|+c}##
##\displaystyle |y-2| = ke^{\ln |x+3|}##, where ##k=e^c##
##\displaystyle |y-2| = k|x+3|##
This is as far as I can get. I am not sure how I can get rid of the absolute value signs in order to obtain a single function.