Linear De

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The integrating factor of dy/dx + y = x is

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1. **Identify Linear coefficients**: For $\frac{dy}{dx} + P(x)y = Q(x)$:
   - Here, $P(x) = 1$ and $Q(x) = x$.
2. **Formula for I.F.**: $I.F. = e^{\int P(x) dx}$.
3. **Calculation**:
   - $I.F. = e^{\int 1 \, dx} = e^x$.
- Multiplication by $e^x$ turns the left side of the original equation into a single derivative: $\frac{d}{dx}(y \, e^x)$.

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