Higher Algebra Hall & Knight Undetermined Coefficients (Chapter 22) Solutions
Hall and Knight Higher Algebra Solutions for Chapter 22 ‘Undetermined Coefficients’ is a perfect study material for engineering entrance exams aspirants. These solutions are designed as per the latest JEE syllabus. They discuss in detail the rationale integral of dimensions, the values of each power and their coefficient, and undetermined coefficients. Some major topics such as homogeneous and nonhomogeneous differential equations, undetermined coefficients, and the method of undetermined coefficients are discussed thoroughly in the chapter. After studying all these concepts deeply you will be able to solve the questions related to the chapter in exams.
Higher Algebra by Hall & Knight Solutions for Undetermined Coefficients have 2 exercises with 27 questions. This chapter holds great importance if you are planning for competitive level exams. By solving these questions, you will be able to find the sum of a series using the method of undetermined coefficients, the conditions that make one algebraic expression divisible by another, the conditions that make an algebraic expression a perfect square and how to expand an expression with ascending powers of x.
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Important Topics for Hall and Knight Higher Algebra Solutions Chapter 22: Undetermined Coefficients
Homogeneous and Nonhomogeneous Differential Equations
A homogeneous differential equation is a differential equation in f(x,y)dy = g(x,y)dx form in case there is a similar degree of f(x,y) and g(x,y).
A function of form F(x,y) that can also be written as knF(x,y) is called a homogeneous function of degree n, for k is not equal to 0.
If we eliminate the constant term of the homogeneous equation then we can find the solution for a linear ordinary differential solution with the help of integration.
In simple terms, if a differential equation is similar to the anonymous function and its derivatives, it is said to be a differential equation.
A second order linear nonhomogeneous differential equation is written as- y”+p(t)y’+q(t)y = g(t). Here g(t) is a non zero function.
However, the associated homogeneous equation is y”+p(t)y ‘+q(t)y = 0 and is also known as a complementary equation.
Method of Undetermined Coefficients
There are undetermined coefficient methods to find the solution to the equations like-
d2y/dx2 + p(x) dy/dx +q(x)y = f(x)
We can solve the equation in two ways: the general solution of homogeneous equation i.e. d2y/dx2 + p(x) dy/dx +q(x)y = 0 or particular solution of nonhomogeneous equation i.e. d2y/dx2 + p(x) dy/dx +q(x)y = f(x)
Exercise Discussion of Hall and Knight Higher Algebra Solutions Chapter 22: Undetermined Coefficients
- There are overall two exercises in the Higher Algebra By H.S. Hall and S.R. Knight Solutions of Undetermined Coefficients.
- The first exercise that has 15 questions in it covers the essential topics from the chapter like methods of coefficient, finding conditions, or proving identities.
- The questions that you will answer in this exercise are like finding the sum of the given terms using the undetermined coefficient method, or finding the conditions if the given term may be a perfect cube, etc
- The second exercise has an overall 12 questions. These questions are based on topics like finding the coefficient of given terms and expansion of terms.
- You will have to answer questions such as expanding the following expressions in ascending power of x as far as x3.
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- We provide solutions in a step by step manner and easy language for your better understanding.
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