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Solve : (dy)/(dx) sqrt(1+x+y) =x+y-1...

Solve : `(dy)/(dx) sqrt(1+x+y) =x+y-1`

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To solve the differential equation \(\frac{dy}{dx} \sqrt{1+x+y} = x+y-1\), we will follow a systematic approach. ### Step 1: Substitute to Remove the Square Root Let \( z^2 = 1 + x + y \). Then, we have: \[ y = z^2 - 1 - x \] Now, differentiate both sides with respect to \(x\): ...
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