Use the general solution of x″ + ω2x = 0 given in Problem 7 to show that a solution satisfying the initial conditions x(t0) = x0, x′(t0) = x1 is the solution given in Problem 7 shifted by an amount t0:
7. Given that x(t) = c1 cos ωt + c2 sin ωt is the general solution of x″ + ω2x = 0 on the interval (−∞, ∞), show that a solution satisfying the initial conditions x(0) = x0, x′(0) = x1 is given by
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Chapter 4 Solutions
A First Course in Differential Equations with Modeling Applications (MindTap Course List)