1 . Determine the region(s) of the x-y plane for which the given D.E. would have

solutions that are unique according to the existence theorem . [2]

Also, sketch the solution region .

2. Use Euler’s method to approximate the solution (to four decimal places ) to the given

initial value problem at x = 0.1, 0.2, 0.3 using steps of size 0.1 (i.e h = 0.1 ) .

. [ hint : f (x, y) = y (2 – y) and ] [3]

3. Find the general solution of the following homogeneous linear differential equation

with constant coefficients. [2]

4. Find the particular solution of the following homogeneous linear differential equation

with constant coefficients. [3]

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