Differential Equations — Class 12 Maths Solution

.: We have $({e^x} + {e^{ - x}})dy - ({e^x} - {e^{ - x}})dx = 0$

$\Rightarrow dy = \cfrac{{{e^x} - {e^{ - x}}}}{{{e^x} + {e^{ - x}}}}dx$
…(1)
Integrating (1) both sides,

we get
$\int d y = \int {\cfrac{{{e^x} - {e^{ - x}}}}{{{e^x} + {e^{ - x}}}}dx} \Rightarrow y = \log |{e^x} + {e^{ - x}}| + C$

which is the required solution.