A calf that weighs x pounds at birth gains weight at the rate of dw/dt = 1200-w, where w is weight in pounds and t in time in years. Solve the differential equation.

W' = 1200 - w

w'⋅ (e^t) + w⋅ (e^t) = 1200⋅ (e^t)

w'⋅ (e^t) + w⋅ (d/dx e^t) = 1200⋅ (e^t)

d/dt [ w⋅ (e^t) ] = 1200⋅ (e^t)

∫ d/dt [ w⋅ (e^t) ] dt = ∫ 1200⋅ (e^t) dt

w⋅e^t = 1200⋅e^t + C

w = [ 1200⋅e^t + C ] ⁄ e^t

w = 1200 + C⋅e^ (-t)

w_o = w (0) = 1200 + C⋅e^ (-0) = 1200 + C

C = w_o - 1200

w = 1200 + (w_o - 1200) ⋅e^ (-t)