-Identify the equilibrium values y'=5\sqrt{5},y>0

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    Equilibrium
In summary, the given ODE has no equilibrium solutions since $y'$ is a constant. The student decided to skip this question and move on to another topic.
  • #1
karush
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$\textrm{ Given $y'=5\sqrt{5},y>0$ answer the following questions.}\\$
$\textrm{a. Identify the equilibrium values.}\\ $
$\textrm{Which are stable and which are unstable?}\\$
$\textrm{b. Construct a phase line. Identify the signs of $y′$ and $y′′$.}\\$
$\textrm{c. Sketch several solution curves.}\\$
ok just posting this now
have deal with it at school
basically clueless
 
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  • #2
karush said:
$\textrm{ Given $y'=5\sqrt{5},y>0$ answer the following questions.}\\$
$\textrm{a. Identify the equilibrium values.}\\ $
$\textrm{Which are stable and which are unstable?}\\$
$\textrm{b. Construct a phase line. Identify the signs of $y′$ and $y′′$.}\\$
$\textrm{c. Sketch several solution curves.}\\$
ok just posting this now
have deal with it at school
basically clueless

Are you sure you copied the question correctly? In the given ODE, there are no equilibrium solutions, since $y'$ is a constant...(Wondering)
 
  • #3
ok sorry, I will just skip this one for now..

I had to go on to another topic anyway.;););)
 

Related to -Identify the equilibrium values y'=5\sqrt{5},y>0

1. What does y'=5\sqrt{5} mean?

The equation y'=5\sqrt{5} represents the derivative of the function y with respect to x. It indicates that the rate of change of y is 5 times the square root of 5.

2. What is the significance of y>0 in this equation?

The inequality y>0 means that the values of y are all positive. In other words, the function y has a range of positive values.

3. How do I find the equilibrium values in this equation?

To find the equilibrium values, you need to set y' equal to 0 and solve for y. In this case, y=0 is the only equilibrium value since the derivative is always positive for y>0.

4. Can there be multiple equilibrium values for this equation?

No, there can only be one equilibrium value for this equation. Since the derivative is always positive, the function y will continue to increase and never reach another equilibrium point.

5. How does the value of y' affect the equilibrium value?

The value of y' does not affect the equilibrium value in this equation. The only equilibrium value is y=0, regardless of the value of y'.

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