sqrt(1+y^2)dx+xyln(x)dy=0

解

1 + y^{2} d x + x y ln (x) d y = 0

y = ln^{2} (ln (x)) - 2 c_{1} ln (ln (x)) + c_{1}^{2} - 1, y = - ln^{2} (ln (x)) - 2 c_{1} ln (ln (x)) + c_{1}^{2} - 1

解答ステップ

1 + y^{2} d x + x y ln (x) d y = 0

分離可能 ODE を解く:

y = ln^{2} (ln (x)) - 2 c_{1} ln (ln (x)) + c_{1}^{2} - 1, y = - ln^{2} (ln (x)) - 2 c_{1} ln (ln (x)) + c_{1}^{2} - 1

y = ln^{2} (ln (x)) - 2 c_{1} ln (ln (x)) + c_{1}^{2} - 1, y = - ln^{2} (ln (x)) - 2 c_{1} ln (ln (x)) + c_{1}^{2} - 1