Given that x(t) = c1 cos omega t + c2 sin omega t is the general solution of x'' + omega2 x=0 on the interval (- ♾️, ♾️), show that a solution satisfying the initial conditions x (0)= x0, x'(0)=x1 is given by X(t)= x0cos omega t + x1/omega sin omega t.
Given that x(t) = c1 cos omega t + c2 sin omega t is the general solution of x'' + omega2 x=0 on the interval (- ♾️, ♾️), show that a solution satisfying the initial conditions x (0)= x0, x'(0)=x1 is given by X(t)= x0cos omega t + x1/omega sin omega t.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 5E
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Given that x(t) = c1 cos omega t + c2 sin omega t is the general solution of x'' + omega2 x=0 on the interval (- ♾️, ♾️), show that a solution satisfying the initial conditions x (0)= x0, x'(0)=x1 is given by
X(t)= x0cos omega t + x1/omega sin omega t.
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