- #1

tracedinair

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## Homework Statement

Find the general solution of the differential equation,

y' + y = be^(-λx)

where b is a real number and λ is a positive constant.

## Homework Equations

y' + P(x)y = Q(x)

Integrating factor: e^(∫P(x) dx)

## The Attempt at a Solution

Let P(x) = 1, Q(x) = be^(-λx)

The equation is already in the form y' + P(x)y = Q(x).

So, the integrating fator is I(x) = e^(∫1 dx) = e^(x)

Multiplying both sides by the integrating factor.

e^(x)y + e^(x)y = be^(-λx)e^(x)

(e^(x)y)' = be^(-λx)e^(x)

Now integrating the left hand side,

e^(x)y = be^(-λx)e^(x)

Here is my problem. I don't know where to go from here. How do I integrate the right hand side? That's my main problem.

Any help will be greatly appreciated.