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Verify that the given functions (explic...

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: `y = x sin x` : `x yprime=y+xsqrt(x^2-y^2)(x!=0`and`x > y or x < y`)

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Given,
`=>y=xsinx and xy'=y+xsqrt(x^2−y^2)`
putting value of y in L.H.S `=>x*(xcosx+sinx)`
`=>x^2cosx+xsinx`
From R.H.S
`=>xsinx+xsqrt(x^2-(xsinx)^2)`
`=>xsinx-x**xsqrt(1-(sinx)^2)`
...
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