Consider the general linear homogeneous second order equation P(x)y + Q(x)y + R(x)y = 0
Chapter 11, Problem 11(choose chapter or problem)
Consider the general linear homogeneous second order equation P(x)y + Q(x)y + R(x)y = 0. (i) We seek an integrating factor (x) such that, upon multiplying Eq. (i) by (x), we can write the resulting equation in the form [(x)P(x)y ] + (x)R(x)y = 0.(a) By equating coefficients of y in Eqs. (i) and (ii), show that must be a solution ofP = (Q P). (iii)(b) Solve Eq. (iii) and thereby show that(x) = 1P(x)exp xx0Q(s)P(s)ds. (iv)Compare this result with that of in Section 3.2.
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