The solution of the differential equation d θ d t = - k θ - θ 0 , where k is constant, is ……

Question

The solution of the differential equation d θ d t = - k θ - θ 0 , where k is constant, is ……, θ = θ 0 + a e - k t, θ = θ 0 + a e k t, θ = 2 θ 0 - a e k t, θ = 2 θ 0 - a e - k t

MARKS App · Accepted Answer

We have differential equation d θ d t = - k θ - θ 0 , where k is constant ⇒ d θ d t + k θ = k θ 0 Which is linear differential equation in form of d y d x + P y = Q ∴ I F = e ∫ k d t = e k t Therefore, required solution, θ e k t = ∫ e k t × k θ 0 d t ⇒ θ e k t = e k t θ 0 + a ⇒ θ = θ 0 + a e - k t

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