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Y(x) = x/(1+cx) ; dy/dx = y^2/x^2

  • Thread starter ziggie125
  • Start date
  • #1
13
0

Homework Statement



Show that each function in the family satisfies the differential equation.
y(x) = x/(1+cx) ; dy/dx = y^2/x^2


The Attempt at a Solution



I'm not sure where to start. I can't see how the integral of dy/dx = y(x)
 

Answers and Replies

  • #2
307
3
Start by taking dy/dx of your y(x) equation, then compare that to y^2/x^2. What do you get?
 
  • #3
13
0
thanks for the reply.

y(x) = x/(1+cx)

dy/dx = ((1+cx) - xc)/(1+cx)^2 = 1/(1+cx)^2

So how does that equal y^2/x^2
 
  • #4
D H
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What is y^2/x^2?
 
  • #5
13
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I'm not sure what you mean. This is all the information i was given for the problem.
 
  • #6
307
3
You have solved dy/dx given that you had started with y(x). That is, you solved the left side of dy/dx = y^2/x^2. Now you have to solve the right side. y^2 = (y(x))^2, try plugging in y(x) to the RHS of that equation and see if the two match up.
 
  • #7
13
0
Click, so you mean,

y^2/x^2 = 1/(1 cx)^2

y^2 = x^2/(1+cx)^2

sqrt(y^2) = sqrt(x^2/(1+cx)^2) = sqrt((x/(1+cx))^2))

y = x/(1+cx)
 
  • #8
307
3
Yes :). But in this case it suffices to just show that y^2/x^2 is the same as dy/dx, which you did in the first step.
 
  • #9
13
0
Alright. Thanks for the help, it is greatly appreciated.
 

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