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### Messages - Doris Zhuomin Jia

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##### Final Exam / Re: FE-P4
« on: December 14, 2018, 11:30:19 AM »
homo: det(A-I𝝀) = (1-𝝀)(-1-𝝀)+2 = 0 ,  𝝀= i, -i
when 𝛌 = i, A-iI = 1-i, -2 ~ 1-i , -2
1, -1-i     0     0
the eigenvector V is span{[2
1-i]}
eitV = (cos(t)+isin(t))V = [2cos(t)+ 2isin(t)
cos(t)-icos(t) + isin(t)+sin(t)]
[x,y] = c1[2cos(t)        +  c2[2sin(t)
cos(t)+sin(t)]          -cos(t)+sin(t)]

𝟇(t) = 2cos(t)         2sin(t)
cos(t)+sin(t)   -cos(t)+sin(t)
Let 𝜱(t)·u' = g(t)
2cos(t)            2sin(t)       sec(𝑡)
cos(t)+sin(t)   -cos(t)+sin(t)    0

2u'1cos(t) + 2u'2sin(t) = sec(t)
u'1cos(t)+u'1sin(t) -u'2cos(t)+u'2sin(t) = 0

u2 = ∫(cos(t)+sin(t))/2cos(t)) =1/2(t-ln|cos(t)|)+C1
u1 = ∫-1/2(cos(t) = -1/2sin(t)+C2

x  = [-1/2sin(t)+C2           ] [2cos(t)       2sin(t)]
y      [ 1/2(t-ln|cos(t)|)+C1][cost+sint   -cos(t)+sin(t)]

2
##### Final Exam / Re: FE-P5
« on: December 14, 2018, 10:55:45 AM »
Sorry i don't know how to type math symbols, so I do part c.

3
##### Final Exam / Re: FE-P5
« on: December 14, 2018, 10:15:12 AM »
a) 𝑥(3𝑥+2𝑦−30)=0,𝑦(2𝑦−𝑥−6)=0
The critical points are (0,0), (0,3), (10,0) and (6,6)

4
##### Final Exam / Re: FE-P3
« on: December 14, 2018, 09:50:28 AM »
homo: r3 - 2r2 - r+2 = 0
(r-1)(r+1)(r-2) =0   r = 1, -1, 2
y1= et   y2=e-t   y3=e2t

W(t,y) = et       e-t     e2t
et      -e-t    2e2t
et       e-t    4e2t
= et(-e-t·4e2t-e-t·2e2t) - e-t(et· 4e2t- et· 2e2t）+ e2t(et·e-t+et·e-t)
= -6e2t - 2e2t + 2e2t =-6e2t
W1 = e-t·2e2t+e-t·e2t= et
W2 = et· 2e2t - et·e2t  = e3t
W3 = et· -e-t -  et·e-t = -2

u1 = ∫ [(2e2t/et +1)·et]/-6e2t = -2ln|et+1| +C1
u2 = ∫[(2e2t/et +1)·e3t]/-6e2t = 2et-e2t+3 -2ln|et+1| +C2
u3 = ∫[(2e2t/et +1)·(-2)]/-6e2t =4(-ln|et+1|+t)+C3

y= u1y1+u2y2+u3y3
y= et(-2ln|et+1| +C1)+e-t(2et-e2t+3 -2ln|et+1| +C2)+e2t(4(-ln|et+1|+t)+C3)

5
##### Quiz-7 / Re: Q7 TUT 0801
« on: November 30, 2018, 07:44:34 PM »
There is my solution

6
##### Term Test 1 / Re: TT1 Problem 2 (morning)
« on: October 16, 2018, 11:27:14 AM »
Hi, there is my solution for Problem 2

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