## Why does this blow up?

I'm looking at the BVP:

$$y'' + ay' + e^{ax}y = 1$$,

with y(0) = 0 and y(10) = 0.

The numerical solution blows up at certain values of $$a$$. For example, a near 0.089 and a near 0.2302. Why does this happen and how do I predict it?
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 Quote by rsq_a I'm looking at the BVP: $$y'' + ay' + e^{ax}y = 1$$, with y(0) = 0 and y(10) = 0. The numerical solution blows up at certain values of $$a$$. For example, a near 0.089 and a near 0.2302. Why does this happen and how do I predict it?
Erm. I found the problem. Near those values of 'a', there exists a zero eigenvalue of the linear operator. I guess that means that,

$$y'' + ay' + e^{ax}y = 0\cdot u^* = 1$$,

is a possible solution, and thus the eigenfunction $$u^* \to \infty$$ will cause the blowup.

Is this correct? It's been a while since I've done Sturm-Liouville stuff.
 What is x?

## Why does this blow up?

 Quote by jacophile What is x?
$$y=y(x)$$