Find the general solution for the differential equation dx/dt=-3x
Please give a quick explanation on how to do this.
dx/dt = - 3x - First we must separate the variables 1/(-3x) dx = dt - Now we must Integrate both sides ∫ [1/(-3x)] dx = ∫ dt To evaluate ∫ [1/(-3x)] dx , simply use the substitution u = - 3x ∫ [1/(-3x)] dx = -(1/3)Therefore: x = 1/3 + Ae^-3t
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