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What is the integrating factor for the equation dy/dx + 3y = 6x?

Practice Questions

Q1
What is the integrating factor for the equation dy/dx + 3y = 6x?
  1. e^(3x)
  2. e^(-3x)
  3. e^(6x)
  4. e^(-6x)

Questions & Step-by-Step Solutions

What is the integrating factor for the equation dy/dx + 3y = 6x?
  • Step 1: Identify the standard form of the differential equation, which is dy/dx + P(x)y = Q(x). In this case, P(x) = 3 and Q(x) = 6x.
  • Step 2: Find the integrating factor, which is given by the formula e^(∫P(x)dx). Here, P(x) = 3.
  • Step 3: Calculate the integral of P(x): ∫3dx = 3x.
  • Step 4: Substitute the result of the integral into the formula for the integrating factor: e^(∫3dx) = e^(3x).
  • Step 5: Conclude that the integrating factor for the equation dy/dx + 3y = 6x is e^(3x).
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