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Question

Let y= f(x) be the particular solution to the differential equation dy/dx= y² with the initial condition f(1)= 1. Which of the following gives an expression for f(x) and the domain for which the solution is valid?

A. f(x)= (2x-1)/x for x≠0

B. f(x)= (2x-1)/x for x>0

C. f(x)= 1/(2-x) for x≠2

D. f(x)= 1/(2-x) for x<2

Answer 1

The answer is C.

dy/y² = dx

-1/y = x + C

You figure it out from here.