If φ (x) is a differentiable function, then the solution of the differential equation d…

Mathematics · JEE Main · NTA ExamsDifferential Equations

If φ (x) is a differentiable function, then the solution of the differential equation
\(d y+\left\{y \phi^{\prime}(x)-\phi(x) \phi^{\prime}(x)\right\}\) dx = 0 is
  1. \(\mathrm{y}=\{\phi(\mathrm{x})-1\}+\mathrm{ce}^{-\phi(\mathrm{x})}\)
  2. \(\mathrm{y} \phi(\mathrm{x})=\{\phi(\mathrm{x})\}^{2}+\mathrm{c}\)
  3. \(y \mathrm{e}^{\phi(x)}=\phi(x) \mathrm{e}^{\phi(x)}+\mathrm{c}\)
  4. none of these

Answer

(A) y = ( x )-1 + ce ^ - ( x )

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