Problem: Find the behavior of $\frac{d^4y}{dx^4} = \cos(x^2 \frac{d^2y}{dx^2}) + \arctan(x^3 dy/dx) + e^x$ in the limit $ x \rightarrow \infty$ to leading order $x^4$. Please place your final solution in a $\boxed{}$ LaTeX Environment. If there are multiple solutions please separate them with a ;.
Solution: $\boxed{e^x}$