$\"\"$

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Statement :

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If a function is $\"\"$ is a solution of differential equation, then $\"\"$ is also a solution of $\"\"$ .

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$\"\"$

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Consider a differential equation $\"\"$ .

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Let the function is of the form $\"\"$ .

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Consider a function $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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Check whether the function $\"\"$ is a solution of a first order differential equation $\"\"$ or not.

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Consider $\"\"$ .

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Differentiate with respect to $\"\"$ .

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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Since the above statement is true, the function $\"\"$ is a solution of first order differential equation $\"\"$ .

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$\"\"$

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Let the function is of the form $\"\"$ , where $\"\"$ is a constant value.

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Consider $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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Check whether the function $\"\"$ is a solution of a first order differential equation $\"\"$ or not.

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Consider $\"\"$ .

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Differentiate with respect to $\"\"$ .

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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Since the above statement is false, the function $\"\"$ is not a solution of first order differential equation $\"\"$ .

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Therefore, the function $\"\"$ is a solution of first order differential equation $\"\"$ .

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Theerfore, the statement is false.

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$\"\"$

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The statement is false.