The solution of the equation \(\frac{dy}{dx}=3^{y-x}\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{1}{3^{x}}-\frac{1}{3^{y}}=c\)
\(\frac{dy}{dx}=3^{y-x}\)
$⇒\int 3^{-y}dy=\int 3^{-x}dx$
$⇒-\frac{3^{-y}}{\log_e3}=-\frac{3^{-x}}{\log_e3}+C$
$⇒\frac{3^{-x}}{\log_e3}-\frac{3^{-y}}{\log_e3}=C$ [$\log 3 ×C$ = Constant]
$⇒\frac{1}{3^{x}}-\frac{1}{3^{y}}=C$