Final answer:
The differential equation dx · e^4x dy = 0 is solved by recognizing that dy must be zero, indicating that y is a constant.
Step-by-step explanation:
To solve the differential equation dx · e^4x dy = 0 by separation of variables, we first note that the product of dx and e^4x with dy equals zero. This implies that either dx = 0 (which would mean that x is constant) or e^4x dy = 0. However, since e^4x cannot be zero, the only possibility is that dy = 0, which implies that y is constant.
Therefore, the solution to this differential equation is that x can take any value (x ∈ ℝ), and y is constant (y = C, where C is any constant).