# Higher-Order Differential Equations

1. Nov 14, 2009

### recon_ind

1. The problem statement, all variables and given/known data

Find the general solution of the given higher-order differential equation.

d3x/(dt3) - d2x/(dt2) - 4x = 0

2. Relevant equations

Use an auxiliary equation such as m3 - m2 - 4 = 0

3. The attempt at a solution

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2. Nov 14, 2009

### Staff: Mentor

That is the auxiliary equation you want to use. As it turns out, the left side can be factored, yielding (m - 2)(m2 + m + 2) = 0

There are three distinct solutions, so the solution to this homogeneous problem will be x(t) = c1e2t + c2em2t + c3em3t. All you have to do is find the other two constants, m2 and m3.

3. Nov 14, 2009

### recon_ind

So, I should just use the quadratic formula to find the other two solutions?

Thanks man.

4. Nov 14, 2009

### recon_ind

The other two solutions are of the form $$\alpha$$ $$\pm$$ $$\beta$$

5. Nov 14, 2009

### Staff: Mentor

Yes. And yes, the two solutions are of the form a +/- b. One of your values of m will be a + b, and the other will be a - b.