Perturbation Theory help

**tibetan-knight** · October 29th 2009, 02:14 PM

Hi...

The given problem:

$<br /> y\prime-y+\epsilon$ t $y^2=0<br />$

Initial condition of y(0) = 1

And with this I am to compute the first order Pert. Theory Approximation. My question, I'm not sure how to do this with a (t) in the equation. Is it possible or is it a typo?

**Rebesques** · January 18th 2010, 04:28 AM

Originally Posted by tibetan-knight

Hi...

The given problem:

$<br /> y\prime-y+\epsilon$ t $y^2=0<br />$

Initial condition of y(0) = 1

And with this I am to compute the first order Pert. Theory Approximation. My question, I'm not sure how to do this with a (t) in the equation. Is it possible or is it a typo?

Not really, its ok as long as it tends to zero with the initial value t=0.

Now, let $y_0$ solve the initial equation and let $y=y_0+\epsilon y_1$ . By substitution and omitting higher order powers of $\epsilon$ , we get $y_1'-y_1=0$ . Along with $y_1(1)=1$ , we get $y=y_0+\epsilon e^{x}$ .

Do check my calcs, I am always clumsy on Mondays.

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