Question

By method of continuation combined with D'Alembert formula solve each of the following twelve problems (9)--(20). x > 0, x > 0, (9) V V V V (10) V V V V Utt - cuzz = 0, ult=0 = 0, Ut t=0 = cos(2), ( ur=0 = 0, Ut – c?Uzz = 0, ult=0 = 0, Ut\t=0 = cos(), | Uzla=0 = 0, Ut – cʻUzx = 0, ult=0 = 0, Ut|t=0 = sin(x), | ulo=0 = 0, Uit - cʻuzz = 0, ult=0 = 0, Wt1t=0 = sin(x), | Uz|q=0 = 0, Ut – c+Uzz = 0, Ult=0 = cos(x), Utle=0 = 0, ( 42=0 = 0, (11) V V V V (12) V V V V (13) V V

Answer 1

F un-collxx = 0 of t he UCX40) 20 § 46X40) - Os(x) z uerte Ucoot) = 0 80 fx co ; glx) = lesxx g h (t) = 0 as hito ŞO continuation combined with D'Alembert solution is given by UcXqt = $ (fexecu) i fex-et)] +& Santet glede = [0 +0] + " for the Casco).dt · CE = c Sin (t) lat Sm Gt) 7 *** att - cl srcx+ct) + Śr CX-ct)]

uxt) = c [Smixes et + esxsmict - Sinxcesct +8rictes x] _ $o ecset) = lote la amictare] ucxots Smycteesx