The solution of the differential equation, d y d x =(x-y)^ 2 , where y(1)=1 , is:

Mathematics · JEE Main · NTA Exams — Differential Equations

1. \(-\log _{e}\left|\frac{1+x-y}{1-x+y}\right|=x+y-z\)
2. \(\log _{e}\left|\frac{2-x}{2-y}\right|=x-y\)
3. \(\log _{e}\left|\frac{2-y}{2-x}\right|=2(y-1)\)
4. \(-\log _{\mathbf{e}}\left|\frac{1-\mathbf{x}+\mathbf{y}}{1+\mathbf{x}-\mathbf{y}}\right|=\mathbf{2}(\mathbf{x}-1)\)

Answer

(D) - _ e | 1- x + y 1+ x - y |= 2 ( x -1)

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