Q. Solution of $\frac{dy}{dx} = 3^{x + y}$ is
A) $3^{x + y} = c$
B) $3^{x} + 3^{y} = c$
C) $3^{x - y} = c$
D) $3^{x} + 3^{- y} = c$
Explanation
(d)
Given, $3^{- y}dy = 3^{x}dx$
$\Rightarrow$ $\int_{}^{}3^{- y}dy = \int_{}^{}3^{x}dx$
$\Rightarrow$ $\frac{{- 3}^{- y}}{\log 3} = \frac{3^{x}}{\log 3} + k$
$\Rightarrow$ $3^{x} + 3^{- y} = c$, where $c = - k\log 3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.