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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=sqrt(a^2-x^2)x in (-x , a)` : `x+y(dy)/(dx)=0(y!=0)`

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`y=sqrt(a^(2)-x^(2))`………`(1)`
differentiate w.r.t.x
`(dy)/(dx)=(1)/(2sqrt(a^(2)-x^(2)))*(-2x)=(-x)/(y)` [from equation `(1)`]
`implies y*(dy)/(dx)=-x`
`implies x+y*(dy)/(dx)=0`
Therefore, `y=sqrt(a^(2)-x^(2))` is the solution of given differential equation.
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