1 Introduction 2 First Order Differential Equations 3 Systems Of Two First Order Equations 4 Second Order Linear Equations 5 The Laplace Transform 6 Systems Of First Order Linear Equations 7 Nonlinear Differential Equations And Stability 8 Numerical Methods A Matrices And Linear Algebra expand_more
4.1 Definitions And Examples 4.2 Theory Of Second Order Linear Homogeneous Equations 4.3 Linear Homogeneous Equations With Constant Coefficients 4.4 Mechanical And Electrical Vibrations 4.5 Nonhomogeneous Equations; Method Of Undetermined Coefficients 4.6 Forced Vibrations, Frequency Response, And Resonance 4.7 Variation Of Parameters 4.P1 A Vibration Insulation Problem 4.P2 Linearization Of A Nonlinear Mechanical System 4.P3 A Spring-mass Event Problem 4.P4 Euler–lagrange Equations expand_more
Problem 1P: (a) If
and ,
show that .
(b) Assuming that is a fundamental matrix for and that, use the result... Problem 2P: In each of Problems 2 through 5, use the method of variation of parameters to find a particular... Problem 3P: In each of Problems 2 through 5, use the method of variation of parameters to find a particular... Problem 4P: In each of Problems 2 through 5, use the method of variation of parameters to find a particular... Problem 5P: In each of Problems 2 through 5, use the method of variation of parameters to find a particular... Problem 6P: In each of Problems 6 through 9, find the solution of the specified initial value problem:
The... Problem 7P: In each of Problems 6 through 9, find the solution of the specified initial value problem:
The... Problem 8P: In each of Problems 6 through 9, find the solution of the specified initial value problem:
The... Problem 9P: In each of Problems 6 through 9, find the solution of the specified initial value problem:
The ... Problem 10P: In each of Problems 10 through 13, use the method of variation of parameters to find a particular... Problem 11P: In each of Problems 10 through 13, use the method of variation of parameters to find a particular... Problem 12P: In each of Problems 10 through 13, use the method of variation of parameters to find a particular... Problem 13P: In each of Problems 10 through 13, use the method of variation of parameters to find a particular... Problem 14P: In each of Problems 14 through 21, find the general solution of the given differential equation.
In... Problem 15P: In each of Problems 14 through 21, find the general solution of the given differential equation. In... Problem 16P: In each of Problems 14 through 21, find the general solution of the given differential equation. In... Problem 17P: In each of Problems 14 through 21, find the general solution of the given differential equation. In... Problem 18P: In each of Problems 14 through 21, find the general solution of the given differential equation.
In... Problem 19P: In each of Problems 14 through 21, find the general solution of the given differential equation. In... Problem 20P: In each of Problems 14 through 21, find the general solution of the given differential equation. In... Problem 21P: In each of Problems 14 through 21, find the general solution of the given differential equation. In... Problem 22P: In each of Problems 22 through 27, verify that the given functions y1 and y2 satisfy the... Problem 23P: In each of Problems 22 through 27, verify that the given functions and satisfy the corresponding... Problem 24P: In each of Problems 22 through 27, verify that the given functions and satisfy the corresponding... Problem 25P: In each of Problems 22 through 27, verify that the given functions and satisfy the corresponding... Problem 26P: In each of Problems 22 through 27, verify that the given functions y1 and y2 satisfy the... Problem 27P: In each of Problems 22 through 27, verify that the given functions y1 and y2 satisfy the... Problem 28P: In each of Problems 28 through 31, find the general solution of the nonhomogeneous Cauchy-Euler... Problem 29P: In each of Problems 28 through 31, find the general solution of the nonhomogeneous Cauchy-Euler... Problem 30P: In each of Problems 28 through 31, find the general solution of the nonhomogeneous Cauchy-Euler... Problem 31P: In each of Problems 28 through 31, find the general solution of the nonhomogeneous Cauchy-Euler... Problem 32P: Show that the solution of the initial value problem
,
,
can be written as , where and are... Problem 33P: By choosing the lower limit of integration in Eq. (27) in the text as the initial point , show that ... Problem 34P: (a) Use the result of Problem 33 to show that the solution of the initial value problem
, ,
... Problem 35P: Use the result of Problem 33 to find the solution of the initial value problem L[y]=(Da)(Db)y=g(t),... Problem 36P: Use the result of Problem 33 to find the solution of the initial value problem
,
Note... Problem 37P: Use the result of Problem 33 to find the solution of the initial value problem L[y]=(Da)2y=g(t),... Problem 38P: By combining the results of the problems 35 through 37, show that the solution of the initial value... Problem 39P: The method of reduction of order (see the discussion preceding problem in section ) can also be... Problem 40P: In each of problems 40 and 41, use the method outlined in problem 39 to solve the given differential... Problem 41P: In each of problems and , use the method outlined in problem to solve the given differential... format_list_bulleted