Verify that the function y = cos x + C (explicit or implicit) is … - Vidyadip

Question

Verify that the function y = cos x + C (explicit or implicit) is a solution of differential equation y' + sin x = 0.

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Answer

Given: y = cos x + C ....(i)
To prove: y is a solution of the differential equation y' + sin x = 0 ...(ii)
Proof: From eq. (i),
y' = -sin x
L.H.S. of eq. (ii),
y' + sin x = -sin x + sin x = 0 = R.H.S.
Hence, y given by eq. (i) is a solution of y' + sin x = 0.

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