Differential Equations
Linear Differential Equations
Premium Question
Grade 12
Question:
If the integrating factor of $\frac{dy}{dx} + \frac{y}{x} = x^2$ is $x^n$, then the value of $n$ equals _____.
Step-by-Step Solution
Key Concept: Compute the integrating factor directly as $e^{\int P(x) \, dx}$ where $P(x) = \frac{1}{x}$, and simplify the resulting exponential.
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Correct Answer: 1