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Who is asking: Student Level: All Question: The ODE dy/dx + 0.5y = 0.5e^{1.5x} ; y(5) = 2 Solve the ODE subject to the given condition using exact methods and evaluate the solution y for x = 5 x=5.2 x=5.4 x=5.6 x=5.8 x=6 I think i should use an integrating factor but i cant do it. I hope someone can help. 

Hi David, First you need to solve the homogenous equation
You can solve this equation using the integration factor
I actually looked at the equation as
and realized that y is a function which is almost identical to its own derivative so I substituted
into the equation and found that
In either case you get the general solution of the homogenous equation to be
Now you need one solution of
Since the right side is 0.5e^{1.5x} I guessed a solution of the form
Substitute this into dy/dx + 0.5y = 0.5e^{1.5x} and solve for A. When I did this I got A =  0.5. Hence the general solution of
is
Harley


