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→Non-separable (non-homogeneous) first-order linear ordinary differential equations: Sweeping changes Tags: Reverted 2017 wikitext editor |
→Non-separable (non-homogeneous) first-order linear ordinary differential equations: Made differentiation of integrating factor more explanatory Tags: Reverted Visual edit |
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We choose this integrating factor because it has the special property that its derivative is itself times the function we are integrating, that is:
:<math>\frac{d\mu}{dx} = e^{\int_{x_0}^x p(t)\, dt} \ \underbrace{\frac{d}{dx} \int_{x_0}^x p(t)\, dt}_{p(x)} = \mu p(x)</math>
Multiply both sides of the original differential equation by {{mvar|μ}} to get:
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