Exact Solution for Linear ODE with Initial Condition

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The discussion focuses on solving the linear ordinary differential equation (ODE) given by dy/dx + 0.6y = 0.5e^(-1.1x) with the initial condition y(0) = 4. The solution involves finding an integrating factor, which is essential for linear ODEs. The integrating factor for this equation is e^(0.6x), allowing for the rearrangement and integration of the equation. The final solution can be evaluated at specified points, particularly from x = 0 to x = 0.5 in increments of 0.05.

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Consider the ODE

dy/dx + 0.6y = 0.5e^(-(1.1)x) , y(0) = 4

solve the ODE subject to the given condition using exact methods and evaluate the solution y for x = 0.0 (0.05) 0.5, (i.e from x = 0 to x = 0.5 in steps of 0.05)

I am terrible with ODEs and would greatly appreciate help in rearranging and staring off this question. I am sure its not terribly difficult but to me it is. Thanks in advance.
 
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Well, it's linear so start by finding an integrating factor.
 

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