Can you help me find the leading asymptotic behaviors about the irregular singular point $x=0$ of $$x^4 \frac{d^2y}{dx^2}+ \frac{1}{4}y=0$$
So far I have got $y(x) = c_{1}8\exp(2/x)+c_{2}8\exp(-2/x)$, is this on the right track for the answer?
Can you help me find the leading asymptotic behaviors about the irregular singular point $x=0$ of $$x^4 \frac{d^2y}{dx^2}+ \frac{1}{4}y=0$$
So far I have got $y(x) = c_{1}8\exp(2/x)+c_{2}8\exp(-2/x)$, is this on the right track for the answer?