Consider the ordinary differential equation $$y''+\frac{yy'}{x^4}+y'^2 = 0, \text{ } \text{ }y(0) = 1 \text{ , } y'(0) = 0 $$
By considering all dominant balances as $x \to 0$, determine whether or not the equation admits a unique solution near $x = 0$.
I am very unfamiliar with dominant balances. Does anyone have any suggestions on how to proceed, or know any good resources to practice problems like these?