Question 1 Find the general solution of d' y +2 +3v=xex +.x2+ 2. dx2 dx [9 marks] Question 2 Find a suitable integrating factor (x) or u(y) and show that the following differential equation is exact by multiplying integrating factor. Find the particular solution. [9 marks] ( y + x sinx)dx + (xln x + xe )dy = 0, y(n) =0. Question 3 Consider the solution of dy dy dx 2 dx + x y =0 in the form of power series in x about xo = 0, i.e., y= >c x" . Find the first six nonzero terms of this series solution. [12 marks]