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

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Sum

Solve the following differential equation.

`(dθ)/dt  = − k (θ − θ_0)`

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Solution

`(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)`

  Is there an error in this question or solution?
Chapter 8: Differential Equation and Applications - Exercise 8.3 [Page 165]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Differential Equation and Applications
Exercise 8.3 | Q 1.2 | Page 165
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