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Question
In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-
y = cos x + C y' + sin x = 0
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Solution
We have,
y' + sin x = 0 .....(1)
Now,
y = cos x + C
⇒ y' = −sin x
Putting the above value in (1), we get
LHS = −sin x + sin x = 0 = RHS
Thus, y = cos x + C is the solution of the given differential equation.
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