Question

Solve the differential equation $(e^x+e^{-x})dy-(e^x-e^{-x})dx=0$

Answer 1

$dy=\frac{e^x-e^{-x}}{e^x+e^{-x}}dx$

integrating on both sides, we have

$\int dy=\int \frac{e^x-e^{-x}}{e^x+e^{-x}}dx$

Put $e^x+e^{-x}=t⟹(e^x-e^{-x})dx=dt$

$\therefore \int dy=\int \frac{1}{t}dt$

$\therefore y=logt+c$

Substituting value of $t$, we have

$y=log(e^x+e^{-x})+c$

This is the required solution.