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

  • Thread starter Thread starter karush
  • Start date Start date
  • Tags Tags
    Equilibrium
karush
Gold Member
MHB
Messages
3,240
Reaction score
5
1000
$\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
 
Last edited:
Physics news on Phys.org
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)
 
ok sorry, I will just skip this one for now..

I had to go on to another topic anyway.;););)
 
Thread 'Direction Fields and Isoclines'
I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
Back
Top