Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation: `y=xsinx : x y^(prime)=y+x sqrt(x^2-y^2)`

Explanation

`y=x sin x`


Differentiating the equation with respect to x,


`y^{prime}=frac{d}{d x}(x sin x) `


`Rightarrow y^{prime}=sin x cdot frac{d}{d x}(x)+x cdot frac{d}{d x}(sin x) `


`Rightarrow y^{prime}=sin x+x cos x`


Put the value of` y^{prime}` in the differential equation,


`L.H.S. =x y^{prime} =x(sin x+x cos x) `


`Rightarrow x sin x+x^{2} cos x `


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