Differential equation

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Find the general solution for the differential equation dx/dt=-3x

Please give a quick explanation on how to do this.

Apr 23rd, 2015

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 




Apr 22nd, 2015

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Apr 23rd, 2015
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Apr 23rd, 2015
Jun 23rd, 2017
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