$\"\"$

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The function is $\"\"$ .

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Rewrite the function.

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$\"\"$

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in the above derivative function.

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$\"\"$

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$\"\"$ .

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$\"\"$

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Find orthogonal trajectory.

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Orthogonal family has negative reciprocal slope.

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$\"\"$

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Rewrite the differential equation.

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$\"\"$

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Integrate on each side.

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$\"\"$

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Power rule of integrals : $\"\"$ .

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$\"\"$

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Graph :

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Graph the family of orthogonal trajectories $\"\"$ and $\"\"$ for different values of $\"\"$ .

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$\"\"$

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Observe the graph :

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The curves of curves $\"\"$ and $\"\"$ are orthogonal to each other.

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$\"\"$

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Graph the family of orthogonal trajectories $\"\"$ and $\"\"$ for different values of $\"\"$ is

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$\"\"$ .