$\"\"$

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(a)

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Observe the solution graph,

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The value of the function that is $\"\"$ is positive on its entire domain.

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The differential equation is $\"\"$ .

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As $\"\"$ is positive, value of $\"\"$ depends on $\"\"$ value.

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For $\"\"$ , $\"\"$ .

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Thus the function is decreasing on $\"\"$ .

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But the function is incresing on $\"\"$ by the graph.

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Therefore, option A is does not corresponding differential equation of the given solution graph.

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$\"\"$

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(b)

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The differential equation is $\"\"$ .

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As $\"\"$ is positive, value of $\"\"$ depends on $\"\"$ value.

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For $\"\"$ , $\"\"$ .

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$\"\"$ means that the function attains its extema value.

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But the function attains its extema value for $\"\"$ .

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Therefore, option B is does not corresponds to the differential equation of the given solution graph.

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$\"\"$

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(c)

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The differential equation is $\"\"$ .

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As $\"\"$ is positive, value of $\"\"$ depends on $\"\"$ value.

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For $\"\"$ , $\"\"$ .

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Thus, the function is increasing on $\"\"$ .

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For $\"\"$ , $\"\"$ .

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Thus, the function is decreasing on $\"\"$ .

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The graph satisfies the above two conditions.

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Therefore, option C is corresponds to the differential equation of the given solution graph.

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$\"\"$

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Option C corresponds to the differential equation of the given solution graph.

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