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Solve the given differential equation by separation of variables: dx· e⁴xdy = 0

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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).

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