I'm using the pertubation method to solve an ODE. And I just need a small clarification.
When I'm solving for the boundary Layer solution I got the following equation:
$$(Y^{''}_0+\epsilon Y_1^{''}+...)+\epsilon \bar{x}(Y^{'}_0+\epsilon Y_1^{'}+...)-(Y^{}_0+\epsilon Y_1^{}+...)=-e^{\bar{x}\epsilon}$$
My question is, when comparing the coefficients of $\epsilon^0$ should it be
$Y^{''}_0-Y_0=-e^{\bar{x}\epsilon}\qquad$ or is it $\qquad Y^{''}_0-Y_0=0$
Appreciate your help