Quandaries and Queries


Who is asking: Student
Level: All

I have a question that i really cant do, it is as follows:

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

dy/dx + 0.5y = 0

You can solve this equation using the integration factor

e-integral(0.5)dx = e-0.5x

I actually looked at the equation as

dy/dx = -0.5y

and realized that y is a function which is almost identical to its own derivative so I substituted

y = eax

into the equation and found that

a = -0.5

In either case you get the general solution of the homogenous equation to be

y = k e-0.5x

Now you need one solution of

dy/dx + 0.5y = 0.5e-1.5x

Since the right side is 0.5e-1.5x I guessed a solution of the form

y = A e-1.5x

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

dy/dx + 0.5y = 0.5e-1.5x


y = k e-0.5x - 0.5 e-1.5x




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