请问这个微分方程如何求解?
发布网友
发布时间：2022-04-23 22:50
共2个回答
热心网友
时间：2023-06-10 14:20
灞曞紑鍏ㄩ儴
热心网友
时间：2023-06-10 14:21
灞曞紑鍏ㄩ儴y'+ay +b鈭歽= 0
dy/dx = -(ay +b鈭歽)
-鈭玠y/(ay +b鈭歽) = 鈭玠x
x = -鈭玠y/(ay +b鈭歽)
= -(2/a)ln|a鈭歽+b| + C
ln|a鈭歽+b| = -(a/2)(x-C)
a鈭歽+b = e^[-(a/2)(x-C)]
y = [ {e^[-(a/2)(x-C)] -b }/a ]^2
let
u=鈭歽
= dy/(2鈭歽)
dy = 2u
鈭玠y/(ay +b鈭歽)
=鈭?u/(au^2 +bu)
=2鈭玠u/(au +b)
=(2/a)ln|au+b| + C'
=(2/a)ln|a鈭歽+b| + C'
