How to solve
M dx + N dy = 0 is exact when My = Nx. Then dF = M dx + N dy with F = C.
Steps
- Compute ∂M/∂y and ∂N/∂x.
- Integrate M in x; fix g(y) using N.
Example
M=2x+y, N=x+2y
- My=Nx=1.
- F=x²+xy+y².
Answer: 1 or x^2+xy+y^2
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M dx + N dy = 0 is exact when My = Nx. Then dF = M dx + N dy with F = C.
Steps
Example
M=2x+y, N=x+2y
Answer: 1 or x^2+xy+y^2