What Are the Values of k That Satisfy This Differential Equation?

[sristi]

I missed class last Thursday and I am completely confused about the homework. I tried reading the text but there aren't any example problems like this one. Anyone know any free resources for James Stewart Single Variable Calculus?

Well here is the question:

For what values of k does the function y=cos kt satisfy the differential equation 4y"=-25y.
For those values of k, verify that every member of the family of functions y=A sin kt + B cos Kt.

I tried solving for y" and setting the equations equal to each other. To tell the truth I don't understand what the question is saying.

Thanks for any help!

 

[greisen]

Have you tried to solve the equation directly

y'' = -k^2*cos(kt)
y = cos(kt)

than you get two values of k +/-.

 

[HallsofIvy]

For a problem where you are asked "show that A is a solution to problem B", actually solving the problem is overkill. Suppose you were asked to show that x= 1 is a solution to the equation x⁵- 3x⁴+ 2x³- 4x²+ 3x- 1= 0. Would you solve the equation or just substitute 1 for x and see if the resulting equation is true?

sristi, substute cos(kt) into 4y"= 5y and see what happens. For what values of k is the resulting equation true?