Integration using separation of variables.

**AmberLamps** · April 21st 2010, 12:21 PM

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):

$dx/dt+ax = b - cx$

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

thanks for any help.

**Danny** · April 21st 2010, 02:25 PM

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):

$dx/dt+ax = b - cx$

What is really confusing to me is what variables I am actually seperating because all I will have on one side is $\int dt$ 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

$<br /> \frac{dx}{dt} = b - (a+c)x<br />$

so

$<br /> \frac{dx}{b - (a+c)x} = dt.<br />$

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