Problem: Find the WKB approximation up to the second leading order for the specific differential equation as $x\to 0$ $3x^5y'''=y$ 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 (not arbitrary constants) in a $\boxed{}$ latex environment.
Solution: $\boxed{y(x) \approx x^{5/3} \left( 1.9461391296842614 e^{-\frac{3^{2/3}}{2}x^{-2/3}} + e^{\frac{3^{2/3}}{4}x^{-2/3}}\left(-1.4641592737823024 \cos\left(\frac{3^{7/6}}{4}x^{-2/3}\right) + 1.3969897071670665 \sin\left(\frac{3^{7/6}}{4}x^{-2/3}\right) \right) \right)}$