Q. 53.8( 4 Votes )

Form the differential equation of the family of curves,

x = A cos nt + B sin nt, where A and B are arbitrary constant.

Answer :

As the given equation has two different arbitrary constants so we can differentiate it twice with respect to x.

x = A cos nt + B sin nt

On differentiating with respect to t we get,

Again, differentiating with respect to x,

As x = A cos nt + B sin nt

Hence, is the required differential equation.

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