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Question
Solve the following differential equation.
`(dθ)/dt = − k (θ − θ_0)`
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)`
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