The solution of the differential equation
\[
\frac{dy}{dx}
=
\frac{3^{x+y}-2\cdot3^x}
{3^{x+y}-2\cdot3^y}
\]
when
\[
y(1)=2
\]
is:
Show Hint
Whenever expressions such as \(a^{x+y}\) appear in a differential equation, first rewrite them as \(a^x\cdot a^y\). This often reveals a hidden separable structure and greatly simplifies the problem.