# Verify that the Given Functions (Explicit Or Implicit) is a Solution of the Corresponding Differential Equation Y = X Sin X : Xy′ = Y+X - Mathematics

verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation

y = x sin x  : xy′ = y + xsqrt(x^2 - y^2) (x != 0 and x > y, or x < -y)

#### Solution

y = x sin x

Differentiating both sides of this equation with respect to x, we get:

Hence, the given function is the solution of the corresponding differential equation.

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#### APPEARS IN

NCERT Class 12 Maths
Chapter 9 Differential Equations
Q 6 | Page 385