I don't why al=(2n-1)pi/2. Can you please explain it to me?Thank you
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Extracted text: 10:58 АМ Тhu May 6 * 56% AA bartleby.com + M (108) - F G cascade yar... M (38,939) - s... y! Yahoo PM Trigonometri... Solve the bo... = bartleby Q Search for textbooks, step-by-step explanatio... Ask an Expert Math / Bundle: Differential Equations w... / Solve the boundary-value problem a 2 d 2 u d x 2 = d 2 u d t 2 , 0 < x="">< l="" ,="" t="" &...="" :="" solve="" the="" boundary-value="" problem="" a="" 2="" d="" 2="" u="" d="" x="" 2="d" 2="" u="" dt="" 2,0="">< x="">< l="" ,t=""> 0 ... X (x) = c8 sin (ax) (11) Differentiate the above equation with respect to x. X' (x) = ac6cos (ax) Substitute L for x in the above equation. X X' (L) = = ac8cos (aL) ac8cos (aL) = 0 (x' (L) = 0) (2n – 1) 5 (2n – 1) aL a = Therefore, the Eigen values are as follows An = an = ((2n – 1) ) Substitute the value of a in equation (11). X (x) = cg sin ((2n – 1) TX 2L The above equation represents the Eigen functions where. n = 1, 2, 3, .... Substitute a? for 1 in equation (6). T" + a²a?T = 0 The general solution of the above equation is as follows: T (t) = c9cos (aat) + c10sin (aat) (12) Differentiate the above equation with respect to t. T' (t) = -aac9 sin (aat) + aac10 cos (aat) Substitute 0 for t in the above equation. X GET 10 FREE QUESTIONS ) (T' (0) = 0)