(a) Show that the solution (7) of the general linear

Chapter 2, Problem 26

(choose chapter or problem)

(a) Show that the solution (7) of the general linear equation (1) can be written in theformy = cy1(t) + y2(t), (i)where c is an arbitrary constant.(b) Show that y1 is a solution of the differential equationy+ p(t)y = 0, (ii)corresponding to g(t) = 0.(c) Show that y2 is a solution of the full linear equation (1). We see later (for example,in Section 3.5) that solutions of higher order linear equations have a pattern similar toEq. (i).Bernoulli Equations. Sometimes it is possible to solve a nonlinear equation by making achange of the dependent variable that converts it into a linear equation. The most importantsuch equation has the formy+ p(t)y = q(t)yn,and is called a Bernoulli equation after Jakob Bernoulli. 27 through 31 deal withequations of this type.