|
查看: 1556|回复: 10
|
differential equation
[复制链接]
|
|
|
a differential equation has y=e^(3x) and y=xe^(3x) as solution
a)find the differential equation
b)write down the general solution of the differential equation anddetermine the particular solution satisfying the initial conditions y=1and dy/dx=0 when x=0 |
|
|
|
|
|
|
|
|
|
|
|
发表于 14-1-2010 10:35 AM
|
显示全部楼层
|
|
|
|
|
|
|
|
|
|
|
发表于 14-1-2010 11:34 AM
|
显示全部楼层
借楼主的楼问问题...
second order differential equation...
y"-4y'+4y=4e^(2x)
我找到
yc=e^2x(a+bx)
现在要找yp
用y= 4e^(2x)
然后我要let y=?
我每会到这边我就不会了...
|
|
|
|
|
|
|
|
|
|
|
|
发表于 14-1-2010 02:35 PM
|
显示全部楼层
a) y"-6y'+9y=0 is one of the differential function.
b) y=Aexp(3x)+Bxexp(3x), use the initial conditions to find A and B. |
|
|
|
|
|
|
|
|
|
|
|
楼主 |
发表于 14-1-2010 08:49 PM
|
显示全部楼层
|
|
|
|
|
|
|
|
|
|
|
发表于 15-1-2010 12:05 AM
|
显示全部楼层
|
|
|
|
|
|
|
|
|
|
|
楼主 |
发表于 16-1-2010 01:19 PM
|
显示全部楼层
|
|
|
|
|
|
|
|
|
|
|
发表于 16-1-2010 02:38 PM
|
显示全部楼层
是什么？我看不到。
數學神童 发表于 16-1-2010 01:19 PM  a) y"-6y'+9y=0 is one of the differential function.
b) y=Aexp(3x)+Bxexp(3x), use the initial conditions to find A and B.
antimatter 发表于 14-1-2010 02:35 PM 
antimatter应该是回复你的问题 |
|
|
|
|
|
|
|
|
|
|
|
楼主 |
发表于 16-1-2010 09:34 PM
|
显示全部楼层
|
why we use y=Aexp(3x)+Bxexp(3x) at part b?isnt the differential equation has repeated roots? |
|
|
|
|
|
|
|
|
|
|
|
发表于 17-1-2010 12:23 AM
|
显示全部楼层
我想应该是这样
我现在学的
2nd order... |
|
|
|
|
|
|
|
|
|
|
|
发表于 17-1-2010 01:18 AM
|
显示全部楼层
|
There is a theorem stating that if there are two solutions satisfying homogeneous second order differential equation, then the general solution should be the linear combination of that two solutions. To see this, you can try substituting your general solution into your differential equation, differentiate them and then you will show that they will finally equal to zero, which is on your right hand side. |
|
|
|
|
|
|
|
|
|
| |
 本周最热论坛帖子
|
变色卡
千斤顶
2022 
78
