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In each of the following verify that the...

In each of the following verify that the given function (explicit or implicit) is a solution of the corresponding differentia equation: `y=xsinx` ii. `\ y=sqrt(a^2-x^2)`

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Given, `y=xsinx`
`implies (dy)/(dx)=y'=(d)/(dx)(x sin x)`
`implies y'=sinx*(d)/(dx)x+x(d)/(dx)(sinx)`
`implies y'=x cosx+sinx`
`impliesxy'=x^(2)cosx+xsinx`
`implies =xsqrt(x^(2)cos^(2)x)+y=xsqrt(x^(2)(1-sin^(2)x))+y`
`=xsqrt(x^(2)-y^(2))+y`
Therefore, `y=x sin x` is the solution of given differential equation.
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