7ху`-sqrt(xy)=7y
(7xy`)/7x=(7y/7x)+(sqrt(xy)/7x)
y`=y/x+(sqrt(xy)/7x)
dy/dx=y/x+(sqrt(xy)/7x)
dy/dx=y/x+(1/7)*sqrt(y/x) => замена y(x)/x,откуда u(x)=xy(x); dy/dx=u+x*du/dx
u+x*du/dx=y+(1/7)*sqrt(u)
du/sqrt(u)=(1/7)dx/x
int(du/sqrt(u))=(1/7)*int(dx/x)
u^(1/2)/(1/2)=(1/7)*lnx+lnC
2sqrt(y/x)=(1/7)*lnx+lnC

А как дальше ответ записать?

int(du/sqrt(u))=(1/7)*int(dx/x)
u^(1/2)/(1/2) = (1/7) * ln |x| + C
2 * u^(1/2) = 1/7 * ln |x| + C
2 * (y/x)^(1/2) = 1/7 * ln |x| + C
Вот и ответ.