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)`
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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