The solution of the differential equation (1+y^ 2 ) d x= [ ^ -1 y-x ] d y is :

Mathematics · JEE Main · NTA Exams — Differential Equations

1. \(\mathbf{x}=\left[\tan ^{-1} \mathbf{y}+1\right]+\frac{\mathbf{c}}{\mathbf{e}^{\tan ^{-1} \mathbf{y}}}\)
2. \(\mathbf{x}=\left[\tan ^{-1} \mathbf{y}-1\right]+\frac{\mathbf{c}}{\mathbf{e}^{\tan ^{-1} \mathbf{y}}}\)
3. \(\mathbf{x}=\left(\tan ^{-1} \mathbf{y}-1\right)-\frac{\mathbf{c}}{\mathbf{e}^{\tan ^{-1} \mathbf{y}}}\)
4. none of these

Answer

(B) x = [ ^ -1 y -1 ]+ c e ^ ^ -1 y

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