Thread: Differential Slope Field Help

Consider the differential equation dy/dx=xy^2
A) on the axes provided sketch a slope field for the given differential equation at the nine points indicated [(-1,-1) (-1,0) (-1,1) (0,-1) (0,0) (0,1) (1,-1) (1,0) (1,1)]
B)find the general solution of the given differential equation in terms of aconstant C
C)Find the particular solution of the differential condition that satisfies the initial condition y(0)=1
D) For what values of the constant C will the solutions of the differential equation have on or more vertical asymptotes? Justify your answers

I have no idea where or how to begin Please Help!

anybody? i figured out part A

Originally Posted by rawkstar

Consider the differential equation dy/dx=xy^2
A) on the axes provided sketch a slope field for the given differential equation at the nine points indicated [(-1,-1) (-1,0) (-1,1) (0,-1) (0,0) (0,1) (1,-1) (1,0) (1,1)]

For the first point (-1, -1) find dy/dx



Through the point (-1, -1) sketch a short segment with slope -1

Do the same for each of the other points

already did, thanks though
I'm just still confused with B C & D although I did get a little hint

Originally Posted by rawkstar

Consider the differential equation dy/dx=xy^2
B)find the general solution of the given differential equation in terms of aconstant C
I have no idea where or how to begin Please Help!

Thank you, I'm pretty sure I can figure out C from that.
I'm not sure how to do D though, I know you get a vertical asymptote when the denominator equals 0 or is undefined. However I'm not sure to do that when you don't know x and theyre asking for values of C

Originally Posted by rawkstar

Consider the differential equation dy/dx=xy^2
A) on the axes provided sketch a slope field for the given differential equation at the nine points indicated [(-1,-1) (-1,0) (-1,1) (0,-1) (0,0) (0,1) (1,-1) (1,0) (1,1)]
B)find the general solution of the given differential equation in terms of aconstant C

is equivalent to . Integrate both sides.

C)Find the particular solution of the differential condition that satisfies the initial condition y(0)=1

Your answer to B will, of course, include a "constant of integration. Set x= 0, y= 1 and determine what that constant is.

D) For what values of the constant C will the solutions of the differential equation have on or more vertical asymptotes? Justify your answers

Presumably your solution to B will be of the form y= a rational function with both x and C in the denominator. For what values of C is there some value of x that makes the denominator 0?

I have no idea where or how to begin Please Help!