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Solve the following differential equation. θθθdθdt =−k(θ−θO) - Mathematics and Statistics

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प्रश्न

Solve the following differential equation.

`(dθ)/dt  = − k (θ − θ_0)`

योग
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उत्तर

`(dθ)/dt  = − k (θ − θ_0)`, k is constant.

∴`(dθ)/ (θ − θ_0) = -k dt`

Integrating on both sides, we get

`int(dθ)/ (θ − θ_0)  = -k int dt`

∴ log |θ − θ0| = - kt + c

∴ θ − θ0 = `e ^(-kt+c)`

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 8: Differential Equation and Applications - Exercise 8.3 [पृष्ठ १६५]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 8 Differential Equation and Applications
Exercise 8.3 | Q 1.2 | पृष्ठ १६५

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