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Solve the following.
Solve: (dy)/(dx) = 1 - xy + y - x
Solve:
$\frac{dy}{dx} = 1 - xy + y - x$
Answer
Answer
$\frac{dy}{dx} = (1 + y) - x(1 + y) = (1 + y)(1 - x)$
Separating the variables: $\frac{dy}{1+y} = (1 - x)\,dx$
Integrating: $\log|1 + y| = x - \frac{x^2}{2} + C$
Hence $\log|1 + y| = x - \frac{x^2}{2} + C$.
Final answer: $\log|1+y| = x - \frac{x^2}{2} + C$