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.
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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