展开 ((y+xy^3)dx+xdy=0) 3/y

解答

展开

((y + x y^{3}) d x + x d y = 0) \frac{3}{y}

3 y^{2} x d x + 3 d x + \frac{3 x d y}{y} = 0

求解步骤

((y + x y^{3}) d x + x d y = 0) \frac{3}{y}

= \frac{3}{y} ((y + y^{3} x) d x + 0 = x d y)

使用分配律:

a (b + c) = ab + a c

a = \frac{3}{y}, b = (y + x y^{3}) d x, c = x d y = 0

\frac{3}{y} (y + x y^{3}) d x + \frac{3}{y} x d y = 0

\frac{3}{y} (y + y^{3} x) d x + \frac{3}{y} x d y = 0

乘开

\frac{3}{y} (y + y^{3} x) d x + \frac{3}{y} x d y : 3 y^{2} x d x + 3 d x + \frac{3 x d y}{y}

3 y^{2} x d x + 3 d x + \frac{3 x d y}{y} = 0

e x p an d A (3, - 3) y B (- 1, - 1)

s im pl i f y (- 3 - 4 i)^{6}

e x p an d \frac{3 x + 5}{( 6 x + 2 ) ( x - 4 )}

s im pl i f y (- 3 - 4 i)^{5}

e x p an d t (1 - (t + 1) e - t)