A question about uniqueness of initial conditions

mech-eng
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Hİ. How can we sure that the initial conditions , say, for a second-order linear equation must be unique which is also the uniqueness of the solution.
 
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I think I just answered this in the thread "a property of differential equations" so I won't repeat all. Please read that.

However, I'm not sure what you mean by "the initial conditions must be unique". Are you simply referring to the uniqueness of the solution satisfying initial conditions.
 
HallsofIvy said:
I think I just answered this in the thread "a property of differential equations" so I won't repeat all. Please read that.

However, I'm not sure what you mean by "the initial conditions must be unique". Are you simply referring to the uniqueness of the solution satisfying initial conditions.

Yes, it is about uniqueness theorem from the initial conditions viewpoint.
 
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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