Consider the differential equation $\frac { d y } { d x } = \frac { y ^ { 2 } } { x - 1 }$. (a) On the axes provided, sketch a slope field for the given differential equation at the six points indicated. (b) Let $y = f ( x )$ be the particular solution to the given differential equation with the initial condition $f ( 2 ) = 3$. Write an equation for the line tangent to the graph of $y = f ( x )$ at $x = 2$. Use your equation to approximate $f ( 2.1 )$. (c) Find the particular solution $y = f ( x )$ to the given differential equation with the initial condition $f ( 2 ) = 3$.
Consider the differential equation $\frac { d y } { d x } = \frac { y ^ { 2 } } { x - 1 }$.\\
(a) On the axes provided, sketch a slope field for the given differential equation at the six points indicated.\\
(b) Let $y = f ( x )$ be the particular solution to the given differential equation with the initial condition $f ( 2 ) = 3$. Write an equation for the line tangent to the graph of $y = f ( x )$ at $x = 2$. Use your equation to approximate $f ( 2.1 )$.\\
(c) Find the particular solution $y = f ( x )$ to the given differential equation with the initial condition $f ( 2 ) = 3$.