y ytgx secx

Ответ от Inspiration[гуру]
y' + y*tg(x) = sec(x)
y'*sec(x) + y*tg(x)*sec(x) = sec²(x)
(y*sec(x))' = sec²(x) --> y*sec(x) = tg(x) + C --> y = sin(x) + C*cos(x)
y'' = y'eʸ
y' = t; y'' = tt'
tt' = teʸ; t(t' - eʸ) = 0 --> t = 0; t' = eʸ; t = eʸ + C
t = 0 --> y = C
t = eʸ + C --> dy/(eʸ + C) = dx --> y/C - ln(eʸ + C)/C = x + C₂