Question

Решите срочна!!!

y'=e^(x+y)+e^(x-y)

y(0)=0

Answer 1

$y' = e^x(e^y+e^{-y})\\ frac{dy}{e^y+e^{-y}} =e^xdx\\ frac{e^ydy}{a^{2y}+1} =e^xdx\\ arctg(e^y)=e^x + C\\ y(0)=0\\ arctg(e^0)=e^0+C=0\\ frac{ pi }{4} =1+C\\ C= frac{ pi -4}{4} \\ arctg(e^y)=e^x- frac{4- pi }{4}$