Use D'Alembert's Formula

Utt means the second derivative with respect to t
Uxx means the second derivative with respect to x

Utt = 4Uxx,   -(inf) < x < (inf),  t > 0
U(x,0) = x,
Ut(x,0) = xe^(-x^2)  for -(inf) < x < (inf)

Please use D'Alembert's Formula and show all work.
If there is Fourier series, please show how you got eigenvalues and eigenvectors. Also, please check your answer and make sure it is correct.
Thank you