Find the Domain (y+1)dx=2x(yd)y

Problem

(y+1)*d(x)=2*x*y*d(y)

Solution

1. Rewrite the differential equation in the standard form d(y)/d(x) to identify the function ƒ(x,y)

d(y)/d(x)=(y+1)/(2*x*y)

2. Identify the constraints for the expression to be defined. The denominator of the rational expression must not be equal to zero.

2*x*y≠0

3. Solve the inequality for the variables x and y This implies that neither variable can be zero.

x≠0

y≠0

4. Express the domain in set-builder notation. The domain consists of all points (x,y) in the Cartesian plane such that x is non-zero and y is non-zero.

D={[(x,y)∈ℝ2,x≠0,y≠0]}

Final Answer

Domain={[(x,y)∈ℝ2,x≠0,y≠0]}

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