Find the Domain xuux+yuuy=3u

Problem

x∂(u)/∂(x)+y∂(u)/∂(y)=3*u

Solution

1. Identify the type of equation as a first-order linear partial differential equation (PDE).

2. Determine the domain of the independent variables x and y based on the structure of the equation.

3. Observe that the coefficients of the partial derivatives are x and y and the right-hand side is 3*u

4. Conclude that there are no square roots, logarithms, or denominators containing variables that would restrict the values of x or y

5. Define the domain as the set of all ordered pairs (x,y) in the two-dimensional real plane.

Final Answer

Domain={(x,y)∈ℝ2}

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