Решить ДY y'tgx-y=5 при y(Пи\4)=0

вот я начал делать но незнаю правильно или нет??

y'tgx-y=5

(dy/dx)*tgx-y=5

tgx*dy=(5+y)dx

(dy)/(5+y)=dx/tgx

и что дальше делать то(((((

интеграл брать от левой и правой части

ln|y+5|=ln|sinx|
y=sinx+5+С

при х=п/4
5+1/корень из 2+С=0
С=-5-1/кореньиз2
у=sinx-1/кореньиз2

вот так?

Теперь проверьте, подставив свой ответ в исходное уравнение

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