Solution of $\frac{dy}{dx}=2^{y-x}$ is :

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

Solution of $\frac{dy}{dx}=2^{y-x}$ is :

Options:

$2^{-y}+2^{-x}=k$

$2^{-y}=k-3.2^{-x}$

$2^{-y}-2^{-x}=k$

$2^{-y}-5.2^{-x}=k$

Correct Answer:

$2^{-y}-2^{-x}=k$

Explanation:

The correct answer is Option (3) → $2^{-y}-2^{-x}=k$

$\frac{dy}{dx}=\frac{2^y}{2^x}$

$⇒\int\frac{1}{2^y}dy=\int\frac{1}{2^x}dx$

$⇒2^{-y}-2^{-x}=k$ [k = constant]