I have another question.

Show that is a solution to this equation, and then solve the initial value problem.

hmm, how do you go about this one?

I thougt the solution would be on the form

since the solution to the homogenous equation

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- Jul 23rd 2009, 06:44 AM #1
## Another question

I have another question.

Show that is a solution to this equation, and then solve the initial value problem.

hmm, how do you go about this one?

I thougt the solution would be on the form

since the solution to the homogenous equation

- Jul 23rd 2009, 07:18 AM #2
Be careful! The auxiliary equation is

So the complimentary solution will have the form .

Now, (via annihilator approach as described here - try to fill in what's missing), the particular solution is of the form

So, it follows that

Thus,

Comparing coefficients, we have

From this, it follows that

So the solution will have the form .

Now apply the initial conditions to find and

Can you take it from here?

- Jul 23rd 2009, 07:29 AM #3

- Jul 23rd 2009, 07:58 AM #4

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When a question is expressed like this you generally just show that the suggested solution is in fact a solution.

So put:

Then;

Then:

As required.

What this shows is that is a particular integral for this ODE. To find the solution to the IVP you now need only solve the homogeneous ODE add its general solution to the PI and apply the initial conditions.

CB