[問題] 微積分問題 煩請高手解答

[readjogood (reading)]

 1)  Derive the general solution for the following model of differential
     equation.

                Z = 1/6 - 3X + Y

               dX/dt = -1/2(m-Z)

               dY/dt = 3/4(Z-Y)

     where m is an exogeneous variable.

   (這題是指對Z微t等於多少嗎?  or???    orz)

2) Consider the CES production function, Q = A[bK^(-p) + (1-b)L^(-p)]^(-1/p) ,

   where A > 0 , 0 < b < 1      -1 < p 且不等於0.

   Given constant input prices r and w, show that the

   locus of points (K*,L*) that minimize the cost, C = rK +wL at various

   levels of Q (i.e.,expansion path) is a straight line emanating from

   the point of origin in the (K,L) space.

  (題目是指對其用lagrange　得的答案後會過原點嗎???    or? )



3) Find  the  general  solution for the difference equation

   Y    +  1/4 Y  =5
    t+2         t

  (是用叉分方程嗎??)




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推 guteres:第一題第三式移一下代入第一式再對t微分再把第二
→ guteres:個式子代入再微分一次再把Z代換掉
→ guteres:這是我的作法
→ guteres:最後Y會先解出跟著解出Z再解出X
→ guteres:PS:Y應該是一個三階的微分方程
推 LCANYA:第三題有給初始條件嗎?
推 readjogood:第三題沒初始條件　題目就這樣了...
→ readjogood:謝謝樓上的諸位高手喔 ^^