Question

РЕБЯТА ПОМОГИТЕ СРОЧНО
БАЛЛАМИ НЕ ОБИЖУ

Answer 1

Ответ:

$y=\frac{1}{8}(arccos(e^{-4e^{2x-5}+C})+1)$

Пошаговое объяснение:

$y'=e^{2x-5}\cdot ctg(8y-1)\\\\\frac{dy}{dx}=e^{2x-5}\cdot ctg(8y-1)\\\\tg(8y-1)dy=e^{2x-5}dy\\\\\frac{sin(8y-1)}{cos(8y-1)}dy=e^{2x-5}dy\\\\\int\frac{sin(8y-1)}{cos(8y-1)}dy\,=\int e^{2x-5}dx \\\\-\frac{1}{8}\int\frac{d(cos(8y-1))}{cos(8y-1)}dy\,=\frac{1}{2}\int e^{2x-5}d(2x-5) \\\\-\frac{1}{8}ln(cos(8y-1))=\frac{1}{2}e^{2x-5} \ \ *(-8)\\\\ln(cos(8y-1))=-4e^{2x-5}+C \\\\cos(8y-1)=e^{-4e^{2x-5}+C}\\\\8y-1=arccos(e^{-4e^{2x-5}+C})\\\\y=\frac{1}{8}(arccos(e^{-4e^{2x-5}+C})+1)$