$\"\"$

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The equation is $\"\"$ .

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Multiply each side by $\"\"$ .

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$\"\"$

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Differentiate on both sides with respective to $\"\"$ .

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$\"\"$

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The R.H.S of the equation is $\"\"$ , because the derivative of the constant is $\"\"$ .

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Consider the L.H.S : $\"\"$

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Use product rule : $\"\"$ .

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$\"\"$

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Replace $\"\"$ with $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Apply cross multiplication.

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$\"\"$

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Now integrate on both sides.

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$\"\"$

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Therefore, $\"\"$ .

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$\"\"$

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The function is $\"\"$ .

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(1) Draw the coordinate plane.

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(2) Graph the function $\"\"$ for several values of $\"\"$ .

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$\"\"$

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The curves $\"\"$ and $\"\"$ represents the orthogonal trajectories.

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The parabolas represent the given family of curves.

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$\"\"$

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Graph :

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$\"\"$