SOLUTION: The differential equation dy/dx = y-3/x-3. produces a slope field with horizontal tangents at y = 3 produces a slope field with vertical tangents at y = 3 produces a slope fie

Question 1030555: The differential equation dy/dx = y-3/x-3.
produces a slope field with horizontal tangents at y = 3
produces a slope field with vertical tangents at y = 3
produces a slope field with rows of parallel segments
I only
II only
I and II
III only
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
I only
----------------------
II cannot be true. The DE is . Letting y = 3 will give (with ), and hence corresponds to horizontal, not vertical tangents.
III cannot be true. Solving for the general solution of ,
==> ln(y-3) = ln(x-3) + lnk for arbitrary k.
==> ln(y-3) = ln(k(x-3)) ==> y-3 = k(x-3).
The general solution yields a family of straight lines that pass through the point (3,3) with the values of the slope varying through all the real numbers. In other words, drawing an arbitrary horizontal line on the cartesian plane will intersect this family at a row of infinite number of points where the (tangential) segments are not parallel, but in which the slopes vary from negative to positive infinity.
RELATED QUESTIONS
solve the differential equation: y dy/dx = x(y^4 + 2(y)^2 + 1) at x= -3 ,... (answered by solver91311,ikleyn)

Which of the following differential equations has the slope field below?... (answered by robertb)

please solve this differential equation : dy/dx=e^(x+y)... (answered by Fombitz)

Please help me with this problem: Find a general solution to the differential equation... (answered by Boreal)

Find a general solution of the differential equation: d^(4)y/dx^(2) -4 d^(3)y/dx^(3)... (answered by fractalier)

A differential equation that is a function of x only will produce a slope field with... (answered by robertb)

sopve the differential equation : (x^2-y^2)*dy=2xy*dx 1. dy*6x+dy(-y^2)=2x^2yd 2. (answered by kekegeter ,robertb)

use the differential equation given by dy/dx=xy/3, y > 0. Find the particular solution y (answered by robertb)

use the differential equation given by dy/dx=xy/3, y > 0. Find the particular solution y (answered by Fombitz)