MHT CET2019Evening ShiftMathematicsDifferential EquationsActual
The solution of the differential equation d θ d t = - k θ - θ 0 , where k is constant, is ……
Options
- Aθ = θ 0 + a e - k t
- Bθ = θ 0 + a e k t
- Cθ = 2 θ 0 - a e k t
- Dθ = 2 θ 0 - a e - k t
Correct answer
A. θ = θ 0 + a e - k t
Step-by-step solution
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