The solution of $(x+y+1)dy=dx$ are:

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Differential Equations

Question:

The solution of $(x+y+1)dy=dx$ are:

Options:

$x+y+2=Ce^y$

x + y + 4 = c log y

log (x + y + 2) = Cy

log (x + y + 1) = C + y

Correct Answer:

$x+y+2=Ce^y$

Explanation:

Put x + y + 1 = t; $1+\frac{dy}{dx}=\frac{dt}{dx}1⇒\frac{dt}{dx}=(\frac{1}{t}+1)⇒\int\frac{-1+(1+t)dt}{1+t}=\int dx$

$⇒-ln(1+t)+t=x+c'$

$⇒-ln(x+y+2)+y+1=c'⇒x+y+2=ce^y$

Or log (x + y + 2)= c₁ + y where c₁ = ln c