Mathematics · Differential Equations
Let M, N, μ, w : ℝ2 → ℝ be differentiable functions with continuous partial derivatives satisfying μ(x,y)M(x,y)dx + μ(x,y)N(x,y)dy = dw. Then which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The equation Mdx + Ndy = 0 is already exact without μ.
- 2μ2 is always the integrating factor.
- 3μ is an integrating factor for the differential equation M(x, y)dx + N(x, y)dy = 0.✓
- 4μ is an integrating factor for Mdx + Ndy = 0 only if w is constant.
Correct answer
μ is an integrating factor for the differential equation M(x, y)dx + N(x, y)dy = 0.
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