Exact differential equation: (2x + y) dx + (x + 2y) dy = 0…

Problem:

Solve the following exact differential equation:

(2x + y) dx + (x + 2y) dy = 0

Requirements:

1. Verify that the equation is exact by checking M/y = N/x.

(Here M = 2x + y, N = x + 2y)

2. Find the potential function F(x, y) such that:

F/x = M and F/y = N

3. Write the general solution in implicit form: F(x, y) = C

Please provide:

– Step-by-step solution with all calculations clearly shown

– No initial/boundary conditions are given, so only the general solution is needed

– Use standard method for exact equations (integrate M wrt x, then add function of y, etc.)

Additional notes:

– I need a detailed, original explanation (not just final answer)

– Preferred method: exact DE solving steps

– Deadline: [apna time daal do, jaise 1 hour ya today]

– Thank you!

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