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Question: Answered & Verified by Expert
The solutions of $(x+y+1) d y=d x$ are
MathematicsDifferential EquationsJEE Main
Options:
  • A $x+y+2=C e^{y}$
  • B $x+y+4=C \log y$
  • C $\quad \log (x+y+2)=C y$
  • D $\log (x+y+2)=C-y$
Solution:
1258 Upvotes Verified Answer
The correct answer is: $x+y+2=C e^{y}$
Putting $x+y+1=u,$ we have $d u=d x+d y$ and the given equation reduces to $u(d u-d x)=$ $d x$

$\Rightarrow \quad \frac{u d u}{u+1}=d x \quad \Rightarrow \quad u-\log (u+1)=x$

$\Rightarrow \log (x+y+2)=y+$ constant

$\Rightarrow x+y+2=C e^{y}$

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