- #1

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## Homework Statement

Hi, I submitted this question on here the other day a user suggested some topics which might help so I have went away and tried this and this is what I have came up with. I just want to know what I have so far is right also I need help with integrating the rhs of the equation.

The question is

dy/dx + 0.8y = 0.6 e

^{-1.4x}y(0)=1

I have to solve the ODE to the given condition using exact methods and evaluate the solution y for x = 0.0 to x=0.5 in steps of 0.05.

## Homework Equations

dy/dx + P(x)y = Q(x)

## The Attempt at a Solution

so I my working so far is

dy/dx + 0.8y = 0.6 e^-1.4x

P(x) = 0.8

IF = e ^

^{∫P(x) dx}

IF = e ^

^{∫0.8 dx}

= e ^

^{0.8x}

e

^{0.8x}* dy/dx + e

^{0.8x}y = e

^{0.8x}*0.6e

^{-1.4x}

Therefore e

^{0.8x}= ∫ e

^{0.8x}*0.6e

^{-1.4x}

This is where I get stuck. What I have done so far is this correct and what should I do to progress from this point? I don't understand how to do the integration on the rhs.