MATH 1950 Lecture 20: Chapter 4.4 - Concavity

Prove that if (r, s) lies on y = f(x), then (cr, s) lies on y = f(x/c).

1 point) If the series y(x) =Σcnx" is a solution of the differential equation 2-2xy+D=0,then cr+2 n-O =0 A general solution of the same equation can be written as y(x) = coy! (x) + cl½(x), where n=2 Calculate a2 = a3 = a4 F bz-

Find a solution of where c is a constant, that satisfies the conditions: (a) (b) (c) y=0 y-0 when x = 0 when too when t y=asin(2cc) + 2a sin(cr) 0