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Definitions Elimination of Arbitrary Constants
Equations of Order
The Existence and Uniqueness of Solutions
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4-lb weight algebra arbitrary constants auxiliary equation characteristic equation complementary function constant coefficients cos2 cosh curve defined dependent variable derivatives determine differential operator E X A M P L E eigenvalues eigenvector elementary equation of order equations with constant EXAMPLE exercises 23 Exercises In exercises exists exponential order exponential shift first-order follows ft/sec function F(t given graph Hence homogeneous equation initial conditions initial value problem integrating factor interval inverse transform l)dx l)dy Laplace operator Laplace transform linear differential equation linear equation linearly independent matrix nonhomogeneous obtain orthogonal trajectories particular solution polynomial result right member roots satisfy set of solutions Show sin2 singular solution sinh solution of equation solution of system Solve the equation spring system X Theorem Verify Wronskian y)dy yields zero