What is the integrating factor of the first-order linear differential equation (dy/dx) + (2/x) y = x^3?

Answer and explanation

Correct answer: C. x^2

  1. Step 1: Standard form is dy/dx + P(x) y = Q(x), where P(x) = 2/x.
  2. Step 2: Integrating factor IF = e^(∫ P(x) dx) = e^(∫ (2/x) dx).
  3. Step 3: ∫ (2/x) dx = 2 ln(x) = ln(x^2).
  4. Step 4: IF = e^(ln(x^2)) = x^2.

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