Consider the differential equation $\frac { d y } { d x } = - \frac { 2 x } { y }$. (a) On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated. (Note: Use the axes provided in the pink test booklet.) (b) Let $y = f ( x )$ be the particular solution to the differential equation with the initial condition $f ( 1 ) = - 1$. Write an equation for the line tangent to the graph of $f$ at $( 1 , - 1 )$ and use it to approximate $f ( 1.1 )$. (c) Find the particular solution $y = f ( x )$ to the given differential equation with the initial condition $f ( 1 ) = - 1$.
Consider the differential equation $\frac { d y } { d x } = - \frac { 2 x } { y }$.
(a) On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated.
(Note: Use the axes provided in the pink test booklet.)
(b) Let $y = f ( x )$ be the particular solution to the differential equation with the initial condition $f ( 1 ) = - 1$. Write an equation for the line tangent to the graph of $f$ at $( 1 , - 1 )$ and use it to approximate $f ( 1.1 )$.
(c) Find the particular solution $y = f ( x )$ to the given differential equation with the initial condition $f ( 1 ) = - 1$.