Consider the differential equation $\frac { d y } { d x } = \frac { y - 1 } { x ^ { 2 } }$, where $x \neq 0$. (a) On the axes provided, sketch a slope field for the given differential equation at the nine points indicated. (Note: Use the axes provided in the exam booklet.) (b) Find the particular solution $y = f ( x )$ to the differential equation with the initial condition $f ( 2 ) = 0$. (c) For the particular solution $y = f ( x )$ described in part (b), find $\lim _ { x \rightarrow \infty } f ( x )$.
Consider the differential equation $\frac { d y } { d x } = \frac { y - 1 } { x ^ { 2 } }$, where $x \neq 0$.\\
(a) On the axes provided, sketch a slope field for the given differential equation at the nine points indicated.\\
(Note: Use the axes provided in the exam booklet.)\\
(b) Find the particular solution $y = f ( x )$ to the differential equation with the initial condition $f ( 2 ) = 0$.\\
(c) For the particular solution $y = f ( x )$ described in part (b), find $\lim _ { x \rightarrow \infty } f ( x )$.