Problem: Find the WKB approximation up to the second leading order for the specific differential equation as $x\to 0$ $x^6 y''' + y = 0$ with initial conditions at $y(1)=1, y'(1)=0, y''(1)=0$ as $x\to 0$. Give ONE final answer in terms of y and x and numbers in a $\boxed{}$ latex environment.
Solution: $\boxed{y(x) \approx x^2 \left( 0.6131324019838598 e^{x^{-1}} + e^{-x^{-1}/2}\left(-0.712093006628941 \cos\left(\frac{\sqrt{3}}{2}x^{-1}\right) -0.8372865406850002 \sin\left(\frac{\sqrt{3}}{2}x^{-1}\right) \right) \right)}$