Problem: Find the leading order behavior of $x^4y'''=y$ subject to boundary conditions $y(1)=1,y'(1)=0,y''(1)=0$ in the limit of $x\to\0^+$.
Solution: $\boxed{y(x) =-0.47991x^{4/3}\exp{\left( \frac{3}{2} x^{-1/3} \right)}\cos\left( \frac{3\sqrt{3}}{2} x^{-1/3} -1.0750 \right) }$