Q. 74.3( 41 Votes )
In each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:
xy = log y + C : 
Answer :
It is given that xy = log y + C
Now, differentiating both sides w.r.t. x, we get,
⇒ y + xy’ = 
⇒ y2 + xyy’ = y’
⇒ (xy – 1)y’ = -y2
⇒ y’ = 
Thus, LHS = RHS
Therefore, the given function is the solution of the corresponding differential equation.
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PREVIOUSIn each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:y = x sin x : xy′ = y + x (x ≠ 0 and x > y or x < – y)NEXTIn each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:y – cos y = x : (y sin y + cos y + x)y′ = y
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