Solving the Linearization Problem for \dot{x}+√x = 0: Expert Suggestions"

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FaroukSchw
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Hello ,
I am trying to linearize \dot{x}+√x = 0. The only equilibrium point is at x=0; but the derivative is not defined at this point. Does anybody have a suggestion?
Regards.
 
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Why are you trying to linearize it?
 
hello Office_Shredder
I just got interested in it when talking to a friend about problems that we can encounter
 
\sqrt{x} cannot be linearized at x= 0 precisely because its derivative does not exist.
 
Thread 'Direction Fields and Isoclines'

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...
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