I need to extract terms in equation which are multiplied with degrees of $a$, $a$ is constant:
$$a\frac{1}{r_0+a r_1+a^2 r_2+a^3 r_3} \cdot \frac{\partial (x_0+ax_1+a^2 x_2+a^3 x_3)}{\partial y}$$
With perturbation methods I will extract terms next to $a^0$ and with some other equation that will be solution of my system for zero approximation, everything next to $a^1$ will be solution for first approximation...
But I don`t know how to extract these terms in denominator with variables $r$. I have solution for this example, for zero approximation-everything(every term) which is multiplied with $a^0$ result is $0$-there are no such terms.
For the first approximation-everything multiplied with $a$ (every term next to $a$-but only this degree of $a$) is one term: $\dfrac{1}{r_0} \dfrac{\partial x_0}{\partial y}$.
I tried with first fraction to use binomial series, but it is not correct results with given solution which I have,