Why is u(x,t)=x(x)t(t). Isn't v(x,t)=x(x)t(t). Can you please explain it to me. Thank you. 10:47 AM Mon May 3* 8% I>AAbartleby.com+GmailSolve the bo...GGoogleN The Real Rea...Derek Chauv...= bartlebyQ Search for textbooks, step-by-step explanatio...Ask an ExpertMath / Bundle: Differential Equations with Boundary-Value Probl... / Solve the boundary-value problem k d 2 u d x 2 = d u ...: Solve the boundary-value problem k a 2 u d x 2 = du dt, 0 < x < 1 , t > 0 u ( 0 ,...Get live help whenever you need from online tutors! Try bartleby tutor today >- ( + w')- = -h[v(1,t) + y (1) – uo]x=1The above expression will be homogeneous if -w' (1) = –hự (1) + huo.Since the value of y (1) = y' (1) is c1 , substitute c¡ for y' (1) in equation –µ' (1) = -hự (1) + huo.-cj =—hсi + huo-c1 + hc1 = huohuoC1 =h-1huoSubstitutefor c1 in equation w (x) = c1X.h-1huoy (x)h-1dvdt0 0,v (0, t) = 0, = -hv (1, t) , h > 0, t> 0 and v (x, 0) = f (x) –The new boundary- value problem is k-dx²huo-x, 0 0(1)dx2dtConsider u (x, t) is X (x) T (t).Substitute X (x) T (t) for u (x, t) in equation (1).(X (x) T (t)) =- (X (x) T (t))dx2dtkX" (x) T (t) = X (x) T' (t)X" (х)k-X(x)T'(1)T(t)X" (х)Consider k-X(x)T'(1)as –1.T(t)Therefore, the equation is reduced as follows:X GET 10 FREE QUESTIONS+λ=0X(x)

Name: Why is u(x,t)=x(x)t(t). Isn't v(x,t)=x(x)t(t). Can you please explain
Uploaded: 2024-03-20T06:46:42.000Z
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Description: Why is u(x,t)=x(x)t(t). Isn't v(x,t)=x(x)t(t). Can you please explain it to me. Thank you. 10:47 AM Mon May 3* 8% I>AAbartleby.com+GmailSolve the bo...GGoogleN The Real Rea...Derek Chauv...= bartlebyQ Search for textbooks, step-by-step explanatio...A