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The solution of the differential equationn `(d theta)/(dt)=-k(theta-theta_(0))` where k is constant, is . . . .A. `theta = theta_(0) + ae^(-kt)`B. `theta = theta_(0) + ar^(kt)`C. `theta = 2theta_(0) - ae^(kt)`D. `theta = 2theta_(0) - ae^(-kt)` |
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Answer» Correct Answer - A We have differential equation `(d theta)/(dt) = - k (theta - theta_(0))`, we where k is constant `implies (d theta)/(dt) + k theta = k theta_(0)` Which is linear differential equation in the form of `(dy)/(dx) + Py = Q` `:. IF = e^(int kdt) = e^(kt)` Therefore required solution, `(theta) (e^(kt)) = int (e^(kt) xx k theta_(0)) dt` `implies theta e^(kt) theta_(0) + a` `implies theta = theta_(0) + ae^(kt)` |
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