6. Most of the problems considered in the text are linear. The equation y'- | yz İs nonlinear, and it is easy to see directly that y tan x is the particular solution for which y(0) 0. Show that b...
7. Consider the differential equation (a) Show that z 0 is a regular singular point of the above differential equation (b) Let y(x) be a solution of the differential equation, where r R and the series converges for any E (-8,s), s > 0 Substitute the series solution y in to the differential equation and simplify the terms to obtain an expression of the form 1-1 where f(r) is a polynomial of degree 2. (c) Determine the values of r....