Consider the general first-order linear differential equation where p(x) and q(x) are...

Consider the general first-order linear differential equation

where p(x) and q(x) are continuous functions on some interval (a, b).

(a) Rewrite Equation (1.9.25) in differential form, and show that an integrating factor for the resulting equation is

b) Show that the general solution to Equation (1.9.25) can be written in the form

where I is given in Equation (1.9.26), and c is an arbitrary constant.