Question

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. $3^x+3^{-y}=c$

Answer 1

The correct option is D $3^x+3^{-y}=c$

Given differential equation is
$\frac{dy}{dx}=3^{x+y}$
$\Rightarrow 3^{-y}dy=3^{x}dx$
On integrating both sides
$\int 3^{-y}dy=\int 3^{x}dx\Rightarrow \frac{-3^{-y}}{\log 3}=\frac{3^x}{\log 3}+k$
$\Rightarrow 3^x+3^{-y}=c$, where $c=-k\log 3$