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). 

(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%)

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

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%)

(a) Apply the divergence theorem to evaluate and S is the surface of the region bounded by the cylinder: r≤5, 0≤ θ ≤ 2π, 0≤ Z≤ 4. (5%)