Dividing throughout by dx to get the equation in the required form, we get:

`(dy)/(dx)+3y=e^(-3x)`

In this example, P(x) = 3 and Q(x) = e−3x.

Now the integrating factor in this exampe is

`e^(intPdx)=e^(int3dx)=e^(3x)`

and

`intQe^(intPdx)dx`

`=inte^(-3x)e^(3x)dx`

`=int1\ dx`

`=x`

Using `ye^(intPdx)=intQe^(intPdx)dx+K`, we have:

ye3x = x + K

or we could write it as:

`y=(x+K)/e^(3x)`

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