# Differential Slope Field Help

• March 27th 2010, 09:32 AM
rawkstar
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

• March 28th 2010, 10:28 AM
rawkstar
anybody? i figured out part A
• March 28th 2010, 10:39 AM
ione
Quote:

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

$\frac{dy}{dx}=(-1)(-1)^2=-1$

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

Do the same for each of the other points
• March 28th 2010, 10:52 AM
rawkstar
I'm just still confused with B C & D although I did get a little hint
• March 28th 2010, 11:08 AM
ione
Quote:

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

$\frac{dy}{dx}=xy^2$

$\frac{dy}{y^2}=x\,dx$

$-\frac{1}{y}=\frac{1}{2}x^2+C$

$y=-\frac{2}{x^2+2C}$
• March 28th 2010, 11:21 AM
rawkstar
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
• March 28th 2010, 02:29 PM
HallsofIvy
Quote:

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

$\frac{dy}{dx}= xy^2$ is equivalent to $\frac{dy}{y^2}= \frac{x dx}$. Integrate both sides.

Quote:

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.

Quote:

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?

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