# Math Help - Perturbation Theory help

1. ## Perturbation Theory help

Hi...

The given problem:

$
y\prime-y+\epsilon$
t $y^2=0
$

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?

2. Originally Posted by tibetan-knight
Hi...

The given problem:

$
y\prime-y+\epsilon$
t $y^2=0
$

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.