Having trouble understanding


by TheAntithesis
Tags: trouble
TheAntithesis
TheAntithesis is offline
#1
Aug13-11, 07:42 PM
P: 14
Concerning the IVP dy/dx = (1 + y^(2)*sinx)/(y(2cosx - 1)) with y(0) = 1

Let f(x,y) = (1 + y^(2)*sinx)/(y(2cosx - 1)). Find a rectangular region in the plane, centred at the point (0,1) and on which the two functions f and f_y are continuous. Explain why the problem has a unique solution on some interval containing 0.

What exactly does this mean? Note that this question comes before the question asking to solve it.
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
HallsofIvy
HallsofIvy is offline
#2
Aug14-11, 07:40 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,904
[tex]f(x,y)= \frac{1+ y^2sin(x)}{y(2cos(x)- 1)}[/tex]
is continuous as long as the denominator is not 0- that is, as long as y is not 0 and 2cos(x)- 1 is not 0 which is same as saying cos(x) is not 1/2.

[tex]f_y(x)= \frac{y^2 sin(x)}{y^2(2cos(x)- 1)}[/tex]
is continuous as long as the denominator is not 0- that is, as long as y is not 0 and cos(x) is not 1/2- the same as the previous condition. Find the largest square, having (0, 1) as center, bounded by y= 0 and x= [itex]\pi/3[/itex] (where cos(x)= 1/2).


Register to reply

Related Discussions
Trouble understanding newtons first law and f=ma Classical Physics 3
Trouble understanding!! Calculus 3
Trouble understanding g-forces General Physics 3
Having trouble understanding this. Classical Physics 7
having trouble w/ understanding pdf... Set Theory, Logic, Probability, Statistics 1