chapter 4

- N-th Order Linear Differential Equations

Pages 60

As we noted earlier, ordinary differential equations are divided into two distinct classes-linear equations and nonlinear equations. In chapters 2 and 3, we studied a few differential equations which can be solved explicitly in terms of elementary functions or which can be written as formulas involving quadratures. In particular, we found that the solution of the first-order linear differential equation yâ€² = a(x)y + b(x) can be written symbolically as y(x) = y1(x)(K + v(x)) where K is an arbitrary constant,

y1(x) = e âˆ« x a(t) dt and v(x) =

âˆ« x b(t) y1(t)

dt.