[理工] [工數]-一階ode "homogeneous"
最近看了ZILL的微方課本
發現HOMOGENEOUS有兩個意思
(1)第一個是在LINEAR DE介紹的那邊看到的
上面寫說
A first-order DE of the form
a1(x)dy/dx + a0(x)y = g(x)
is said to be a linear equation.
When g(x) = 0 ,the linear equation is said to be "homogeneous".
(2)第二個homogeneous是在Solution by substitutions的相關章節碰到
文中寫道:
If, a function f possesses the property f(tx,ty) = t^a f(x,y) for some real
number a then f is said to be a homogeneous function of degree a .
A first-order DE in differential form
M(x,y)dx + N(x,y)dy = 0
is said to be "homogeneous" if both coefficients M and N are homogeneous
function of the same degree.
我知道這兩個HOMOGENEOUS的意思是不一樣的
想請問這兩個HOMOGENEOUS各是代表什麼意思?(我知道其中一個是齊性還是齊次的樣子)
但什麼是齊性(次)呢@@?
有沒有什麼物理意義存在呢?
如果可以的話 可以舉個例子嗎@@?
謝謝回答
感激不盡^^
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