1. ## Perturbation Theory help

Hi...

The given problem:

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

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:

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

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

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