Question

Решите (1+y^2)dx+(1+x^2)dy=0

Answer 1

Разделяем переменные

$(1+y^2)dx+(1+x^2)dy=0 \\ \\ (1+y^2)dx=-(1+x^2)dy \\ \\ - \frac{dy}{1+y^2} = \frac{dx}{1+x^2} \\ \\ - \int\limits {\frac{dy}{1+y^2}} \, dx = \int\limits {\frac{dx}{1+x^2}} \, dx \\ \\ -arctgy=arctgx+C \\ \\ tg(-arctgy)=tg(arctgx+C) \\ \\ tg(arctgy)=-tg(arctgx+C) \\ \\ y=-tg(arctgx+C)$