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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:`x+y=tan^(-1)y` : `y^2y^(prime)+y^2+1=0`

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To verify that the function \( x + y = \tan^{-1}(y) \) is a solution of the differential equation \( y^2 y' + y^2 + 1 = 0 \), we will follow these steps: ### Step 1: Start with the given function We have the equation: \[ x + y = \tan^{-1}(y) \] ...
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