What is the integrating factor for the equation dy/dx + 2y = 3x?
Practice Questions
1 question
Q1
What is the integrating factor for the equation dy/dx + 2y = 3x?
e^(2x)
e^(-2x)
e^(3x)
e^(-3x)
The integrating factor is e^(∫2dx) = e^(2x).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the integrating factor for the equation dy/dx + 2y = 3x?
Solution: The integrating factor is e^(∫2dx) = e^(2x).
Steps: 5
Step 1: Identify the standard form of the first-order linear differential equation, which is dy/dx + P(x)y = Q(x). In this case, P(x) = 2 and Q(x) = 3x.
Step 2: Find the integrating factor, which is given by the formula e^(∫P(x)dx). Here, P(x) = 2.
Step 3: Calculate the integral of P(x): ∫2dx = 2x.
Step 4: Substitute the result of the integral into the formula for the integrating factor: e^(∫2dx) = e^(2x).
Step 5: Conclude that the integrating factor for the equation dy/dx + 2y = 3x is e^(2x).
