Find the solution of y =-k^2*y , y(0)=1 y'(0)=0?

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SUMMARY

The differential equation y'' = -k²y with initial conditions y(0) = 1 and y'(0) = 0 is a standard second-order linear homogeneous equation. The characteristic equation yields complex roots ±ki, leading to the general solution y(t) = A cos(kt) + B sin(kt). Applying the initial conditions results in A = 1 and B = 0, giving the specific solution y(t) = cos(kt). The confusion regarding the characteristic equation is clarified, confirming that the method is valid.

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Find the solution of y"=-k^2*y , y(0)=1 y'(0)=0?

Homework Statement


Find the solution of y"=-k^2*y , y(0)=1 y'(0)=0?


Homework Equations


y"=-k^2*y , y(0)=1 y'(0)=0?


The Attempt at a Solution


I've been stuck on this problem for a while but I can't seem to get it. I used the method of making it into a characteristic equation, but I got +/- ki for R but that doesn't seem to work. Thanks in advance for your help!
 
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Why doesn't it work? Show your calculations.
 
"got +/- ki for R but that doesn't seem to work."

It does work.
 

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