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  • Find the solution of frac{dy}{dx}=2^{y-x}

Find the solution of \frac{dy}{dx}=2^{y-x}

Answers (1)

Given

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

To find: Solution of the given differential equation

Rewrite the equation as,

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

Integrating on both sides,

\int \frac{dy}{2^{y}}=\int \frac{dx}{2^{x}}\\ \\ \int \frac{dx}{a^{x}}=-\frac{a^{-x}}{In a}

Formula:     

- \frac{2^{-y}}{In 2}=-\frac{2^{-x}}{In 2}+c

Here c is some arbitrary constant

2^{-x}-2^{-y}=c\;In\;2\\ 2^{-x}-2^{-y}=d

 d is also some arbitrary constant = c In2

Posted by

infoexpert24

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