Explain what is meant by an integrating factor for an equation of the form
Show that is an integrating factor for
and find the solution such that , for given .
Show that for all and hence that
For a solution with , show graphically, by considering the sign of first for and then for , that for all .
Sketch the solution for the case , and show that property that both as and as from below, where is the positive number that satisfies .
[Do not consider the range .]