Sketch a slope field for the provided differential equation in ~ the twelve suggested points.Sketch the solution curve v the suggest (1, 0). uncover y = f(x) by resolving the differential equation dy/dx = x-1 v the initial condition f(1) = 0
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dy = (x-1) dx

Integrating...

You are watching: Consider the differential equation dy/dx=y^2/x-1

y = (1/2)x^2 - x + c

Per initial condition: (1,0) ,

0 = (1/2)(1)^2 - 1 + c

0 = 1/2 - 1 + c

0 = -1/2 + c

c = 1/2

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


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