In 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)

Question

In 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)

Philoid · Accepted Answer

It is given that y = xsinx

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

⇒ y’ = sinx + xcosx

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

LHS = xy’ = x(sinx + xcosx)

= xsinx + x²cosx

= 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 = x sin x : xy′ = y + x (x ≠ 0 and x > y or x < – y)

In 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)