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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)`
Squaring both sides,
`=>y^2 = a^2-x^2`
Differentiating both sides w.r.t. `x`,
`=>2ydy/dx = 0 - 2x`
`=>ydy/dx = - x`
`=>x+ydy/dx = 0`
So, given function is a solution of the corresponding differential equation.
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