20、Consider the following partial differential equation for the bivariate function v(x, t)
, 0 ≤ x ≤ 10, t ≥ 0
subject to conditions

Express the solution v(x, t) in the following form

for some constants ,  ∈ satisfying 0 ≤ r₀＜r₁＞r₂＜... ＞ 0 for n = 1, 2,... Which of the following statements is/are true?
(A)
(B)
(C)
(D)

(E) None of the above is true.

16. Consider the following second order differential equation3t2y"(t) + sin(t)y'(t) - cos(t)w(t) =0. be two linearly independent Frobeniusseries solution for y(t) in the above differential equation when t ＞ 0. Assuming r1≥ r2and a0 = 1, which of the following statements is/are true regarding the solution y1(t)?(A) r1 =1.(B) (C) (D) (E) None of the above is true.

17.Continue from Question 十六.Assuming b0 = 2, which of the following statements is/aretrue regarding the solution y2(t)?(A) (B) b1=0(C)(D)(E) None of the above is true.

18.Consider the following differential equation for the function y(t) defined for t ≥ 0where u(t) is the usual unit-step (Heaviside) function and where * is the usual convolutionaloperation of two functions. Assume y(t) = 0 for t ＜ 0. Given the initial conditiony(0) = 1, which of the following staterents is/are true regarding the Laplace transformY(s) = ((t)] of solution y(t) in the above equation?(A) Y(s= )= -6(B) Y(s=1)=1(C) Y(s=2)=(D) Y(s=3)=(E) None of the above is true.

19. Continue from Question t十八. Which of the following statements is/are true regardingthe solution y(t)?(A) y'(1) =1(B) y'(π) =1(C) y"(1) = -1(D) y"(π)=0(E) None of the above is true.

1.下列選項,用字完全正確的是:(A)你這一番議論,真可謂之發矇振瞶(B)爺爺說他退休後要去環遊世界,真是老驥伏壢,志在千里(C)他在口試委員面前顯得踟躇不安,不斷呼吸,希望能有好表現(D)當政府財源短詘,應導節開支,避免不必要的浪費。

2.請依文意選出排列順序最為恰當的選項:「西螺平原的海風猛撼著這座甲、意志之塔的每一根神經乙、而鐵釘的齒緊緊咬著,鐵臂的手緊緊握著丙、力的圖案,美的網,猛撼著這座丁、猛撼著,而且絕望地嘯著嚴肅的靜。」(余光中〈西螺大橋〉)(A)甲丁乙丙 (B)丙甲丁乙 (C)丙乙丁甲 (D) 甲丙乙丁

3.下列選項「」內的成語,何者使用正確?(A)顏回雖身居陋巷,「簞食壺漿」,仍不改其樂道之心(B)吳寶春以米釀荔香麵包參加世界麵包大師賽,最後「雀屏中選」,奪得世界冠軍(C)張里長平日熱心助人,「茹柔吐剛」,深受里民的愛戴(D)國君若只是聽信小人的話,遠離賢才,將導致鼠輩猖狂,「黃鐘毀棄」,國家怎麼會有未來呢。

4.下列選項所稱說的人物何者正確?(A)寫鬼寫妖,高人一等。刺貪刺虐,入木三分一施耐庵(B)佛骨謫來,嶺海因而生色。鱷魚徙去,江湖自此澄清-韓愈(C)日帝曰侯曰聖人,名光日月。安蜀安漢安天下,志在春秋-孔明(D)生前欺天絕漢統,死後欺人設疑冢。人生用智死即休,何有餘機到丘壟-曹丕。

複選題5.以下皆是歌頌古代女子的詩句,配對正確的選項是:(A)瓦礫明珠一例拋,何曾石尉重嬌燒?都緣頑福前生造,更有同歸慰寂寥-綠珠。(B)腸斷烏啼夜嘯風,虞兮幽恨對重瞳。黥彭甘受他年醢,飲劍何如楚帳中-西施(C)長劍雄談態自殊,美人巨眼識窮途。屍居餘氣楊公幕,豈得羈縻女丈夫-楊貴妃(D)一代傾城逐浪花,吳宮空自憶兒家。效顰莫笑東村女,頭白溪邊尚浣紗-漢武帝李夫人

6.下列各組「」中的字,字形相同的是哪一選項:(A)撫摩「ㄐㄩˊ」育/笑容可「ㄐㄩˊ」(B)觀「ㄒㄧㄣˋ」伺隙/「ㄒㄧㄣˋ」馬游韁(C)投「ㄏㄨㄢˊ」自盡/撒手人「ㄏㄨㄢˊ」(D)「ㄍㄨㄥ」自菲薄/反「ㄍㄨㄥ」內省