Q. 53.7( 22 Votes )

# In each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:

y = Ax : xy′ = y (x ≠ 0)

Answer :

It is given that y = Ax

Now, differentiating both sides w.r.t. x, we get,

⇒ y’ = A

Now, Substituting the values of y’ in the given differential equations, we get,

xy’ = x.A = Ax = y = 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:NEXTIn 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)

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