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