Solution of $\frac{d y}{d x}=e^{y+x}+e^{

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Differential Equations

Question:

Solution of $\frac{d y}{d x}=e^{y+x}+e^{y-x}$ is :

Options:

$e^x(x+1)=y$

$e^x(x+1)+1=y$

$e^x(x-1)+1=y$

None of these

Correct Answer:

None of these

Explanation:

$\frac{d y}{d x}=e^y . e^x+e^y . e^{-x}=e^y\left(e^x+e^{-x}\right)$

$\Rightarrow e^{-y} dy=\left(e^{x}+e^{-x}\right) dx \Rightarrow e^{-y}=e^{x}-e^{-x}+c$

Hence (4) is the correct answer.