x(y)=u*v, x(y)'=u'*v+u*v'
подставим в x'-x*tg(25y)=sin(50y)
u'*v+u*v'-u*v*tg(25y)=sin(50y)
u'*v+u(v'-v*tg(25y))=sin(50y)
v'-v*tg(25y)=0, v'=v*tg(25y)
dv/v=dy*tg(25y), int dv/v=int dy*tg(25y)
ln|v|=1/25*ln|sec(25*y)|, v=1/25*sec(25*y)
1/25*sec(25*y)*u'=sin(50*y)
du/dy=25*sin(50*y)/sec(25*y)
int du=int 25*sin(50*y)/sec(25*y)dy
u=(-cos(75*y)+3*cos(25*y))/6+C
x=1/25*sec(25*y)*(-cos(75*y)+3*cos(25*y))/6+C
теперь правильно?