Given that x(t) = c¡ cos wt + cz sin wt is the general solution of x" + w²x = 0 on the interval (-*, *), show that a solution satisfying the initial conditions x(0) = xo, x'(0) = xị is given by x(t) = x cos wt + 1 sin ot.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Q10.
Given that x(t) = c, cos wt + c2 sin wt is the general
solution of x" + w?x = 0 on the interval (-*, x),
show that a solution satisfying the initial conditions
x(0) = xo, x'(0) = xi is given by
x(t) = x, cos wt +
-sin wt.
Transcribed Image Text:Q10. Given that x(t) = c, cos wt + c2 sin wt is the general solution of x" + w?x = 0 on the interval (-*, x), show that a solution satisfying the initial conditions x(0) = xo, x'(0) = xi is given by x(t) = x, cos wt + -sin wt.
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