direction field-diiferental equation

Hi, i know how to Sketch the direction field but don't unbdestand the part


Attachment 9693

"Using the direction field decide whether a solution y(x) tends to a finite limit when x goes to infinity. How does this limit depend on the value of the initial condition y(0) ?" (Please look at the attachment)
Can some1 please help me

Quote:

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Originally Posted by nerdo

Hi, i know how to Sketch the direction field but don't unbdestand the part


Attachment 9693

"Using the direction field decide whether a solution y(x) tends to a finite limit when x goes to infinity. How does this limit depend on the value of the initial condition y(0) ?" (Please look at the attachment)
Can some1 please help me

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If you sketched the direction field, the answers should be obvious: sketch a few solutions with various initial conditions, look at what is happening... The direction field gives you the slopes of the solution, so you know when they increase of decrease, this is the main point. Look in particular at what happens when or . These are the "critical" cases.