What is the integrating factor for the equation dy/dx + 3y = 6?
Practice Questions
1 question
Q1
What is the integrating factor for the equation dy/dx + 3y = 6?
e^(3x)
e^(-3x)
3e^(3x)
3e^(-3x)
The integrating factor is e^(∫3dx) = e^(3x).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the integrating factor for the equation dy/dx + 3y = 6?
Solution: The integrating factor is e^(∫3dx) = e^(3x).
Steps: 6
Step 1: Identify the equation you have, which is dy/dx + 3y = 6.
Step 2: Notice that the equation is in the standard form of a first-order linear differential equation: dy/dx + P(x)y = Q(x). Here, P(x) = 3 and Q(x) = 6.
Step 3: Find the integrating factor, which is calculated using the formula e^(∫P(x)dx). In this case, P(x) = 3.
Step 4: Calculate the integral of P(x): ∫3dx = 3x.
Step 5: Now, substitute this result into the formula for the integrating factor: e^(∫3dx) = e^(3x).
Step 6: Therefore, the integrating factor for the equation dy/dx + 3y = 6 is e^(3x).
