CALCULUS: VARIABLES SEPERABLE???????????????????????????!


Question: CALCULUS: VARIABLES SEPERABLE?????????????????????…
How would I solve:

dy/dx = (y-1) / (x^2) with the initial condition y(2) = 0 meaning (2,0)

Thanks!!!

Answers:

dy/dx = (y-1) / (x^2)

divide both sides by (y-1) dx
dy/(y-1) = dx/x^2

Integrate both sides
ln (y-1) = -1/x
y-1 = e^(-1/x)+C ----(1)

substitute x=2; y=0
0-1= e^(-1/2) + C
C = -e^(-1/2)-1

Plug this C into equation (1)

y-1 = e^(-1/x) -e^(-1/2)-1
y = e^(-1/x) - e^(-1/2)



are you telling us that you cannot integrate dy / [ y - 1] = dx / x 2 ??




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