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The solutions of $(x+y+1) d y=d x$ are
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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
$\Rightarrow x+y+2=C e^{y}$
$\Rightarrow \quad \frac{u d u}{u+1}=d x \quad \Rightarrow \quad u-\log (u+1)=x$
$\Rightarrow \log (x+y+2)=y+$ constant
$\Rightarrow x+y+2=C e^{y}$
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