Solve the differential equation dx/dt=-6*x , given when t=0 x=7.
You start by seperating the variables giving,
(1/x)*dx=(-6)*dt
you then integrate both sides with respect to the variables,
ln(x)=-6*t+c
you then subsitute in the given conditions to find 'c',
ln(7)=0+c therefore c=ln(7)
ln(x)=-6t+ln(7)
taking exponential of each element gives:
x=exp(-6t)+7
LC
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