2. Solve the system of differential equations for x(t) and y(t).
(10%)

(2). Discuss at least two (2) but no more than four (4) works of British literature that have shaped your imagination of Britain as an historical place. Name and discuss these works. How have they shaped and informed your ideas about Britain? How do these works express British identity to you and construct Britain as an historical place? Explain with concrete and specific references to the texts.

(3). Discuss at least two (2) but no more than four (4) works by British authors that take place in settings outside the British Isles. Name and discuss these works. Why do you think the authors take an interest in stories or literary material in settings outside Britain? How do these works reflect the author's ideas about foreign places and cultures and Britain's historical and cultural relations to these places and communities? Explain with concrete and specific references to the texts.

(a)(5%)

(b) = 9x. Obtain y(x) that subjects to (5%)

3. Find the series solution of the following differential equation about x = 0.   (10%) You have to express the solution in the form of y(x) = C1y1(x)+ C2y2(x). To save time, you can only show the first five terms of y1(x) and y2(x). 

4. Use the Laplace transform to solve the problem and obtain y(t). (5%)

(a) Find the determinant of M and obtain the inverse matrix .(3%+4%)

(b) Estimate the eigenvalues and eigenvectors of M.(4%+4%)

(a) Let f(x,y) = asin(xy) +x2 +4y2(1 -y). For what values of a will f have a local minimum at (0,0)? (5%)

(b) Let (a≥0). Find I'(a). It is evident that I(0) = 0. Solve I(a). (5%)