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## Homework Statement

a. find the general solution to this differential equation

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

b. find the particular solution to the given initial condition f(0) = 1

c. use the solution found in b to find the range of f

## Homework Equations

none really

## The Attempt at a Solution

this question seemed simple, but i can't really get the right answer.

here is my attempt

*i use different letters after manipulating constants, because they are still constants after adding/subtracting/dividing/multiplying

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

*separation of variables*

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

*integrate both sides*

x^2/2 + C1= -(y-1)^-1 + C2

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

solve for y

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

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

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

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

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

raise everything to the negative 1

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

x^2/2 +G = (x^2 + 2G)/2

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

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

but i can tell already this is the wrong answer, and with a wrong general solution, i can't do the other parts of the problem.