二、 陶淵明詩的題材可分為哪幾類？最多的是哪一類？試舉一些例子加以說明。(25分)

三、 試指出明代四大小說，並就其中二種略述內容大要、主題思想、藝術成就及其影響。(25分)

四、 中國戲曲中有雜劇和傳奇，二者有何異同之處？請比較說明之。(25分)

1. Many marine fish species require n-3 highly unsaturated fatty acid (HUFA) as their essential fatty acid. Fatty acids with high degree of un-saturation are more susceptible to attack from oxygen free radicals than saturated fatty acids. This may increase the requirement of anti-oxidative nutrients. Further, fatty acid composition of dietary lipids has been shown to affect the fatty acid profile and lipid per-oxidation activity in bio-membrane of hybrid tilapia. When dietary HUFA increased, the lipid per-oxidation activity also increased. (Translate this paragraph into Chinese). (25%)

2. What kind of research topic would you like to work on if you are admitted to the Department of Aquatic Biosciences at NCYU? (Answer this question in English) (25%)

3. Aquaculture is defined as “The farming of aquatic organisms including fish, mollusks, crustaceans and aquatic plants. Farming implies some sort of intervention in the rearing process to enhance production, such as regular stocking, feeding, protection from predators, etc. Farming also implies individual or corporate ownership of the stock being cultivated.” For statistical purposes, aquatic organisms which are harvested by an individual or corporate body which has owned them throughout their rearing period contribute to aquaculture, while aquatic organisms which are exploited by the public as a common property resource, with or without appropriate licenses, are the harvest of fisheries. (Translate this paragraph into Chinese) (25%)

4. 將下圖用中文呈現。(25%)

求以下一階一次常微分方程式之通解：(25 分) \[ xdy - [y + xy^3(1 + \ln x)]dx = 0 \]其中 \( \ln x \) 為自然對數函數。

2. 求解以下高階線性微分方程：(25 分) \[ y'' - 2y' + y = 4\sinh^2\left(\frac{x}{2}\right) + 4\cos^2 x. \]

3. 求解以下微分方程之初值問題：(25 分) \[ x^2 y'' - xy' + y = x(\ln x) \] 其中 \( y(1) = 0 \) and \( y'(1) = 0 \) 且 \( \ln x \) 為自然對數函數。

4. 求解以下 Sturm-Liouville 邊界值問題之特徵值與特徵函數：(25 分) \[ (xy')' + \frac{\lambda}{x} y = 0, \quad y(1) = y(e) = 0, \quad \text{其中 } e \text{ 為自然指數常數}。 \]

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