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...versa. In fact the famous Picard theorem [proving the existence and uniqueness of the solution to initial value problem for a first order ode ] is ...

...| = 2 => a^2 = e, 且g in G, g^2= e => g= a (by the condition of uniqueness ) 欲證 ax=xa for all x in G 註: x' 表 inverse of x for all x in...

...b) those ideas allow us to address questions of existence and uniqueness for sulutions of Ax=b 這些想法使我們能解決Ax=b之解...

因為看不懂你的式子 解釋如何解如下 令二個解分別為y1, y2，Wronskians方法是看下面矩陣行列式是否為零 來決定其是否線性相依或獨立 | y1 y2 | W= | | = y1*y2'-y2*y1' | y1' y2' | 若你式子是y1=x^(0.25) 那y1'=0.25*x^(-0.75) y2...

1.方程式 輔助方程式有3根, 0, k, k => (m-0)(m-k)(m-k)=0 => m³-2km²+k²m=0 故原線性ODE為 y'''- 2ky" + ky' =0 2.線性獨立(此題應設k不為0,否則題目錯誤) (法一)比例法 e^(kx), xe^(kx) 無任何兩個函數比例(quotient)為常數現象,故為線性獨立 (註:此法不嚴謹, 如 1, x+1...

...f(x) Therefore f(x) is a fixed point of g, so by the uniqueness , we have f(x)=x This shows that x is a fixed point...

...where φ(t,x) is the maximal integral curve at x.在存在性 (existence) 和唯一性 ( uniqueness ) 的前提之下，對每一個初始值 (initial value) x 雖然存在無限多個解（各定義...

...on the z-axis for all t > 0.Proof. Say t* > 0. By uniqueness properties (the right-hand side of the ODE is Lipschitz...