A first course in differential equations with applications

Answers to odd-numbered auxiliary equation boundary conditions boundary-value problem capacitor Cauchy-Euler equation Chapter convergence cosh curves damping force defined determine displacement dy dx eigenvalues equation of motion equilibrium position Euler Euler's Method Evaluate EXAMPLE exponential order family of solutions farad first-order equation follows formula Fourier series fundamental set given differential equation graph Hence homogeneous equation indicial equation initial conditions initial-value problem instantaneous velocity interval Laplace transform linear equation linearly independent linearly independent solutions mass mathematics matrix method Miscellaneous Problems nonhomogeneous obtain odd-numbered problems begin ohms ordinary point orthogonal trajectories particular solution piecewise continuous polynomial power series regular singular point result roots satisfies second-order Section separation of variables series circuit series solution set of solutions shown in Figure simple harmonic motion sinh solve the given substitution superposition principle temperature variables vector vibrations Wronskian zero