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FirstOrder Differential Equations
Applications of FirstOrder Differential Equations
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Answers to odd-numbered auxiliary equation boundary-value problem Cauchy-Euler equation CHAPTER converge cos—x cosh damping force defined determine dy dx eigenvalues eigenvector equation of motion equilibrium position Euler formula Euler method EXAMPLE Find EXAMPLE Solve EXERCISES family of solutions first-order equation follows form a fundamental Fourier series fundamental matrix fundamental set given differential equation graph Hence homogeneous system initial conditions initial-value problem instantaneous velocity interval isoclines Laplace transform last equation linearly independent linearly independent solutions mass Method with h obtain odd-numbered problems begin ordinary point orthogonal partial differential equation particular solution polynomials power series preceding example regular singular point roots Runge-Kutta method satisfies second solution Section series solution set of solutions simple harmonic motion sin—x sinh solution vector solve the given substitution superposition principle Theorem tion variables verify vibrations write Wronskian zero