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...
... integral equation, and vice 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 ...
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...