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# Match the differential equation with its direction field (labeled I-IV). Give reasons for your answer.$y' = x(2 - y)$

## $=-1,$ which is true in $1 \mathrm{V}$

#### Topics

Differential Equations

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### Video Transcript

word. Look, you're asked to find So course abrasion were getting his flight minus. Why? Giving slope field one you reading and four determining the correct slope field. Find some delivering solutions of why of this equation If they exist that we know that why one being equilibrium solution and only it have that zero which is equal, like crime people to fine my That's why it is equal to x times who? Nice parole X in the real numbers. And therefore, if X is not before 20 possible the father is that to my city Must be zero or that c has people. So you see that the only delivering solution why does, too there will be accepted, for example, acid too y equals two. You see that no one has this, and so three has swell that so for you. So choices are one of three. The trouble Which of these two correct slope field looking? Some initial value? No, we have initial value. Why you you call zero. You know that the slope at Oregon 00 going to be zero tu minus euro which is equal to you. Go therefore exactly horizontal slow your you see that graph one has one Uncle Slope The origin. The graph three did not refuse. You conclude that correct Field one.

Ohio State University

#### Topics

Differential Equations

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