A First Course in Differential Equations with Applications

amount Answers to odd-numbered applied approximate assume becomes boundary-value problem called Chapter circuit coefficients complex constant containing continuous convergence curves damping defined DEFINITION dependent derivatives described determine differential equation displacement eigenvalues equal equilibrium position Evaluate EXAMPLE Exercises exists fact factor Figure first-order follows force formula Fourier function fundamental given gives graph Hence homogeneous homogeneous function implies indicated initial conditions initial-value problem integral interval known Laplace transform latter linear linearly independent mass mathematics matrix method motion multiple Note obtain odd-numbered problems begin operator ordinary origin orthogonal partial particular solution period respectively result roots satisfies separable shown singular point sinh solution Solve spring steady-state substitution Suppose temperature Theorem variables vector vibrations weight write yields zero