1 Introduction 2 First-order Differential Equations 3 Mathematical Models And Numerical Methods Involving First-order Equations 4 Linear Second-order Equations 5 Introduction To Systems And Phase Plane Analysis 6 Theory Of Higher-order Linear Differential Equations 7 Laplace Transforms 8 Series Solutions Of Differential Equations 9 Matrix Methods For Linear Systems 10 Partial Differential Equations 11 Eigenvalue Problems And Sturm–liouville Equations 12 Stability Of Autonomous Systems 13 Existence And Uniqueness Theory A Appendix A Review Of Integration Techniques expand_more
4.1 Introduction: The Mass-spring Oscillator 4.2 Homogeneous Linear Equations: The General Solution 4.3 Auxiliary Equations With Complex Roots 4.4 Nonhomogeneous Equations: The Method Of Undetermined Coefficients 4.5 The Superposition Principle And Undetermined Coefficients Revisited 4.6 Variation Of Parameters 4.7 Variable-coefficient Equations 4.8 Qualitative Considerations For Variable-coefficient And Nonlinear Equations 4.9 A Closer Look At Free Mechanical Vibrations 4.10 A Closer Look At Forced Mechanical Vibrations 4.RP Review Problems For Chapter 4 expand_more
Problem 1E: In Problems 1-8, the auxiliary equation for the given differential equation has complex roots. Find... Problem 2E: In Problems 1-8, the auxiliary equation for the given differential equation has complex roots. Find... Problem 3E Problem 4E Problem 5E: In Problems 1-8, the auxiliary equation for the given differential equation has complex roots. Find... Problem 6E: In Problems 1-8, the auxiliary equation for the given differential equation has complex roots. Find... Problem 7E: In Problems 1-8, the auxiliary equation for the given differential equation has complex roots. Find... Problem 8E: In Problems 1-8, the auxiliary equation for the given differential equation has complex roots. Find... Problem 9E: In Problems 9-20, find a general solution. y8y+7y=0 Problem 10E: In Problems 9-20, find a general solution. y+4y+8y=0 Problem 11E: In Problems 9-20, find a general solution. z+10z+25z=0 Problem 12E: In Problems 9-20, find a general solution. u+7u=0 Problem 13E: In Problems 9-20, find a general solution. y2y+26y=0 Problem 14E: In Problems 9-20, find a general solution. y+2y+5y=0 Problem 15E: In Problems 9-20, find a general solution. y3y11y=0 Problem 16E: In Problems 9-20, find a general solution. y+10y+41y=0 Problem 17E: In Problems 9-20, find a general solution. yy+7y=0 Problem 18E: In Problems 9-20, find a general solution. 2y+13y7y=0 Problem 19E: In Problems 9-20, find a general solution. y+y+3y5y=0 Problem 20E: In Problems 9-20, find a general solution. yy+2y=0 Problem 21E: In Problems 21-27, solve the given initial value problem. y+2y+2y=0; y(0)=2, y(0)=1 Problem 22E: In Problems 21-27, solve the initial value problem. y+2y+17y=0; y(0)=1, y(0)=1 Problem 23E: In Problems 21-27, solve the given initial value problem. w4w+2w=0; w(0)=0, w(0)=1 Problem 24E: In Problems 21-27, solve the given initial value problem. y+9y=0; y(0)=1, y(0)=1 Problem 25E: In Problems 21-27, solve the given initial value problem. y2y+2y=0; y()=e, y()=0 Problem 26E Problem 27E: In Problems 21-27, solve the given initial value problem. y4y+7y6y=0; y(0)=1, y(0)=0; y(0)=0 Problem 28E: To see the effect of changing the parameters b in the initial value problem y+by+4y=0 ;y(0)=1,... Problem 29E: Find a general solution to the following higher-order equations. a. yy+y+3y=0 b. y+2y+5y26y=0 c.... Problem 30E Problem 31E: Using the mass-spring analogy, predict the behavior as t+ of the solution to the given initial value... Problem 32E: Vibrating Spring without Damping. A vibrating spring without dampening can be modelled by the... Problem 33E: Vibrating Spring with Damping. Using the model for a vibrating spring with dampening discussed in... Problem 34E Problem 35E: Swinging Door. The motion of a swinging door with an adjustment screw that controls the amount of... Problem 36E Problem 37E Problem 38E: Prove the sum of angles formula for the sine function by following these steps. Fix x a) Let... format_list_bulleted