CUET Preparation Today
| The solution of the equation \(\frac{dy}{dx}=3^{y-x}\) is |
\(3^{x}-3^{y}=c\) \(\frac{1}{3^{x}}+\frac{1}{3^{y}}=c\) \(3x+3y=c\) \(\frac{1}{3^{x}}-\frac{1}{3^{y}}=x\) |
| \(\frac{1}{3^{x}}-\frac{1}{3^{y}}=x\) |
| \(\begin{aligned}\int 3^{-y}dy&=\int 3^{-x}dx\\ \frac{-3^{y}}{\log_{e}3}&=\frac{-3^{-x}}{\log_{e}3}+\frac{c}{\log_{e}3}\\ \frac{1}{3^{x}}-\frac{1}{3^{y}}&=c\end{aligned}\) |
