求微分方程dx/y+dy/x=0满足初始条件y(4)=2特解的为？

Question

如题所述

Answer 1

(1/y)dx + (1/x)dy = 0
(1/y)dx = - (1/x)dy
等号两边各乘以 xy
xdx = -ydy
积分
(1/2)x^2 + (C1) = -(1/2)y^2 +(C2)
化简
x^2 +y^2 = C
代入初试条件
4^2+2^2 = C
C = 20
微分方程为
x^2 + y^2 = 20