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FIRST ORDER DIFFERENTIAL EQUATIONS
NONLINEAR DIFFERENTIAL EQUATIONS
9 other sections not shown
algebraic arbitrary constants assume asymptotically stable auxiliary equation Bessel equation c1 and c2 compute consider constant coefficients continuous corresponding critical point damping defined derivatives determine discussed dxjdt dyjdt eigenvalues eigenvectors equation of order Euler equation Euler method example existence and uniqueness formula error fundamental matrix fundamental set given by Eq Hence homogeneous equation indicial equation initial conditions initial value problem integrating factor interval Laplace transform linear combination linear system linearly independent solutions mass mathematical motion multiplication nonlinear obtain order linear equation particular solution point x0 polynomial positive r1 and r2 radius of convergence recurrence relation regular singular point roots satisfies the initial second order linear second solution Section series solution set of solutions Show side of Eq solution of Eq Substituting system of equations Taylor series trajectories variable vectors velocity Verify Wronskian y1 and y2 yp(x zero