The solution of the differential equation d y d x - y+3 x _ e (y+3 x) +3=0 is: (where C…

Mathematics · JEE Main · NTA ExamsDifferential Equations

The solution of the differential equation \(\frac{d y}{d x}-\frac{y+3 x}{\log _{e}(y+3 x)}+3=0\) is:

(where C is a constant of integration)

  1. \(x-2 \log _{1}(y+3 x)=5\)
  2. \(x-\log _{1}(y+3 x)=c\)
  3. \(x-\frac{1}{2}\left(\log _{1}(y+3 x)\right)^{2}=c\)
  4. \(y+3 x-\frac{1}{2}\left(\log _{x} x\right)^{2}=c\)

Answer

(C) x- 1 2 ( _ 1 (y+3 x) )^ 2 =c

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