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Introduction to Differential Equations I
Second and HigherOrder Linear Differential Equations
14 other sections not shown
algebraic assume Bessel Bessel equation boundary value problem calculate called Chapter characteristic equation complex number compute Consider constant coefficients continuous converges d2w d2w defined denote derivative determine eigenvalues eigenvectors equation 12 error Euler method Example farad Figure first-order equations formula Fourier series fundamental matrix fundamental matrix solution gallons given Hence homogeneous equation homogeneous system improved Euler method initial conditions initial-value problem interval inverse Laplace transform linear differential equations linearly independent linearly independent solutions mass mathematics motion Multiplying both sides nirx nonzero obtain particular solution Picard iterations polynomial power series method principal matrix solution proof Prove real numbers result roots Runge-Kutta method second-order equation Section separation of variables Show side of equation solution of equation solution that satisfies Substituting Suppose tank temperature tion unique solution variables vector velocity voltage Wronskian yields zero