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Form the differential equation of the family of curves x=A cos nt+ Bsin nt, where A and B are arbitrary constants.

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Form the differential equation of the family of curves x=A cos nt+ Bsin nt, where A and B are arbitrary constants.

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Equation of the family of curves, x=A cos nt+ Bsin nt, where A and B are arbitrary constants. 

Differentiating the above equation with respect to t on both sides, we have,

This is the required differential equation.

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