Answer
$ -0.2$
Work Step by Step
In order to determine the exact solution, isolate the x and y terms on one side and integrate both sides.
$\int \dfrac{dy}{y^2}=\int (2x-2) dx$ ...(1)
In order to determine the differential equation, we will have to take the derivative of the differential equation.
Equation (2) gives: $(\dfrac{-1}{y}=x^2-2x+c$ ...(2)
Apply the initial conditions, to calculate the value of $c$
$(\dfrac{-1}{2}=2^2-2(2)+c\implies c=2$
Now, equation (2) becomes:
$(\dfrac{-1}{y}=x^2-2x+2$ or, $y=-\dfrac{1}{x^2-2x+2}$
Thus, the exact solution is: $y(3)=-\dfrac{1}{3^2-2(3)+2} = -0.2$
