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Question

Form the differential equation representing the family of curves y = A sin x, by eliminating the arbitrary constant A.

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Solution

Given: y = A sinx


y=A sinx ...1Differentiating both sides with respect to xdydx=A cosxA=1cosxdydxSubstituting the value of A in 1, we gety=1cosxdydx sinxy=sinxcosxdydxy=tanxdydxtanxdydx-y=0

Hence, the differential equation representing the family of curves y = A sinx is tanxdydx-y=0.

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