   Chapter 17, Problem 3RCC

Chapter
Section
Textbook Problem

(a) Write the general form of a second-order nonhomogeneous linear differential equation with constant coefficients.(b) What is the complementary equation? How does it help solve the original differential equation?(c) Explain how the method of undetermined coefficients works.(d) Explain how the method of variation of parameters works.

(a)

To determine

To write: The general form of a second-order nonhomogeneous linear differential equation with constant coefficients.

Explanation

Formula used:

Consider the second-order linear differential equation as follows.

P(x)d2ydx2+Q(x)dydx+R(x)y=G(x) (1)

Here,

P , Q , R , and G are continuous functions.

If G(x) has some polynomial then second-order differential equation is known as nonhomogeneous equation.

P(x)d2ydx2+Q(x)dydx+R(x)y=G(x) (2)

Consider P(x) , Q(x) and R(x) has a constant values represented as a , b and c respectively

(b)

To determine

To explain: The complementary equation and how complementary equation helps to solve the original differential equation.

(c)

To determine

To Explain: How the method of undetermined coefficients works.

(d)

To determine

To Explain: How the method of variation parameter works.

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