# Integration using separation of variables.

• Apr 21st 2010, 12:21 PM
AmberLamps
Integration using separation of variables.
Hey guys,

This is from an econ class so I am really struggling with some of the pure math.

I need to solve the following differential equation use the separation of variables technique (a,b, and c positive constants):

$\displaystyle dx/dt+ax = b - cx$

What is really confusing to me is what variables I am actually seperating because all I will have on one side is $\displaystyle \int dt$ and it doesn't really seem right to me. But I also can't find any similar examples online.

thanks for any help.
• Apr 21st 2010, 02:25 PM
Jester
Quote:

Originally Posted by AmberLamps
Hey guys,

This is from an econ class so I am really struggling with some of the pure math.

I need to solve the following differential equation use the separation of variables technique (a,b, and c positive constants):

$\displaystyle dx/dt+ax = b - cx$

What is really confusing to me is what variables I am actually seperating because all I will have on one side is $\displaystyle \int dt$ and it doesn't really seem right to me. But I also can't find any similar examples online.

thanks for any help.

Try this

$\displaystyle \frac{dx}{dt} = b - (a+c)x$

so

$\displaystyle \frac{dx}{b - (a+c)x} = dt.$