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)

Question

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)

Philoid · Accepted 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.

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)

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)