A curve C is called a flow line of a vector field F if F is atangent vector to C at each

Chapter 15, Problem 47

(choose chapter or problem)

A curve \(C\) is called a flow line of a vector field \(F\) if \(F\) is a tangent vector to \(C\) at each point along \(C\) (see the accompanying figure).

(a) Let \(C\) be a flow line for \(F(x, y) = −yi + x j\), and let \((x, y)\) be a point on \(C\) for which. Show that the flow lines satisfy the differential equation

                    \(\frac{d y}{d x}=-\frac{x}{y}\)

(b) Solve the differential equation in part (a) by separation of variables, and show that the flow lines are concentric circles centered at the origin.

Equation Transcription:

Text Transcription:

C

F

F(x, y) = −yi + x j

(x, y)

y not = 0

dy/dx=-x/y