Determining if a function is an eigenfunction Is the function cos(3x + 5) an eig

Question

Determining if a function is an eigenfunction Is the function cos(3x + 5) an eigenfunction of the operator d2/dx2 and, if so, what is the corresponding eigenvalue? Perform the indicated operation on the given function and see if the function satisfies an eigenvalue equation. Use (d/dx)sin ax = a cos ax and (d/dx)cos ax = -a sin ax. The operator operating on the function yields d2/dx2cos(3x + 5)) = d/dx(-3 sin(3x + 5)) = -9cos(3x + 5) and we see that the original function reappears multiplied by the eigenvalue -9. Is the function e3x+5 an eigenfunction of the operator d2/dx2 and, if so, what is the corresponding eigenvalue?

Explanation / Answer

e3x+5

d2/dx2 (e3x+5) = d/dx(3e3x+5) = 9e3x+5

eigenvalue = 9

Yes function is eigenfunction of operator d2/dx2

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