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An Introduction to Differential Equations
FirstOrder Differential Equations
Applications of FirstOrder Differential Equations
13 other sections not shown
Answers to odd-numbered auxiliary equation Cauchy-Euler equation Chapter complex numbers converge cosh curves damping force defined determine dx dx dy dx dy/dx eigenvalues eigenvector equation of motion equilibrium position Evaluate EXAMPLE Exercises family of solutions Find the differential first-order differential equation first-order equation follows formula Fourier series ft/sec function fundamental set given differential equation graph Hence initial conditions initial-value problem instantaneous velocity integrating factor interval Laplace transform linear equations linearly independent linearly independent solutions mass matrix Miscellaneous problems nonhomogeneous obtain odd function odd-numbered problems begin ordinary differential equations ordinary point orthogonal trajectories particular solution polynomial power series real number regular singular point roots satisfies second-order Section separation of variables series solution set of solutions simple harmonic motion sinh solve the given substitution superposition principle Theorem variables vector Wronskian zero