Math Problem Statement
Solution
The question asks to find the integrating factor of the given first-order linear differential equation:
General Form of a First-Order Linear Differential Equation:
A first-order linear differential equation has the general form: where and are functions of .
Integrating Factor:
The integrating factor () is given by: where is the coefficient of in the equation.
In this case, .
Calculation of Integrating Factor:
Thus, the integrating factor is .
Answer:
The correct option is:
B) .
Would you like more details or have any questions?
Related Questions:
- How do you solve a differential equation after finding the integrating factor?
- Can you explain how the integrating factor method works in general?
- What happens if is not ? How does that change the integrating factor?
- What if the differential equation were non-linear? How would that affect solving it?
- How can you verify that the integrating factor you found is correct?
Tip:
When solving a linear differential equation, always write it in the standard form first to easily identify and apply the integrating factor formula correctly.
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Math Problem Analysis
Mathematical Concepts
Differential Equations
Integrating Factors
Linear Equations
Formulas
Integrating Factor: μ(x) = e^(∫P(x) dx)
Theorems
Integrating Factor Method for First-Order Linear Differential Equations
Suitable Grade Level
Grades 11-12
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