I don't understand why w(x,t)= x+(1-x)t^2

Transcribed Image Text:2:48 PM Sat Apr 17 * 7% I AA bartleby.com X b In Problems 13-16 proceed as in Example 2 to solve the... f Facebook = bartleby Q Search for textbooks, step-by-step explanatio... E Ask an Expert Math / Bundle: Differential Equations with Boundary-Value P... | In Problems 13-16 proceed as in Example 2 to solve the giv... i In Problems 13-16 proceed as in Example 2 to solve the given boundary-value proble... Get live help whenever you need from online tutors! Try bartleby tutor today > The given boundary value problem is, ди + 2t + 3tx dx2 (1) %| dt Consider the equation, u (x, t) = v (x, t)+ y (x, t). (2) By using the formula, у (х, ) %3D и (0, г) +lu (1, 1) — и (0, 0)] In the given boundary value problem L = 1 At given boundary conditions u (0, t) = t² , u (1, t) = 1 and u (x, 0) = x² , y (x, t) = x + (1 – x) t² . Substitute y (x, t) = x + (1 – x) t² in equation (2), u (x, t) = v (x, t) + x + (1 – x) t² . (4) Partially differentiate both sides of the equation (4) with respect to t, ди + 2(1 – x) t dt dt Substitute u dt dv + 2 (1 – x) t and dx2 in equation (1), dt dx2 + 5tx dv dt (5) dx2 When 1 a², a > 0 Consider the equation, v (x, t) = X (x). (6) X GET 10 FREE QUESTIONS (6), X" = -1 II
Transcribed Image Text:2:47 PM Sat Apr 17 * 8% I AA bartleby.com + X b In Problems 13-16 proceed as in Example 2 to solve the... f Facebook = bartleby Q Search for textbooks, step-by-step explanatio... E Ask an Expert Math / Bundle: Differential Equations with Boundary-Value P... | In Problems 13-16 proceed as in Example 2 to solve the giv... i In Problems 13-16 proceed as in Example 2 to solve the given boundary-value proble... Get live help whenever you need from online tutors! Try bartleby tutor today → DIFFERENTIAL EQUATIONS with Problems Bundle: Differential Equations wit.. 9th Edition Dennis G. Zill Publisher: Cengage Learning DENNIS G. ZILA Find 2 ISBN: 9781337604901 Chapter 12.6, Problem 14E Textbook Problem In Problems 13-16 proceed as in Example 2 to solve the given boundary-value problem. ди 14. + 2t + 3tx 0 < x< 1, t> 0 dx2 u(0, t) = 2, u(1, t) = 1, t> 0 %3D u(x, 0) = x², 0 < x<1 Expert Solution To determine The solution of the boundary value problem under given boundary conditions. X GET 10 FREE QUESTIONS

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I don't understand why w(x,t)= x+(1-x)t^2 2:48 PM Sat Apr 17* 7% IAAbartleby.comX b In Problems 13-16 proceed as in Example 2 to solve the...f Facebook= bartlebyQ Search for textbooks, step-by-step explanatio...E Ask an ExpertMath / Bundle: Differential Equations with Boundary-Value P... | In Problems 13-16 proceed as in Example 2 to solve the giv...i In Problems 13-16 proceed as in Example 2 to solve the given boundary-value proble...Get live help whenever you need from online tutors! Try bartleby tutor today >The given boundary value problem is,ди+ 2t + 3txdx2(1)%|dtConsider the equation,u (x, t) = v (x, t)+ y (x, t).(2)By using the formula,у (х, ) %3D и (0, г) +lu (1, 1) — и (0, 0)]In the given boundary value problem L = 1At given boundary conditions u (0, t) = t² , u (1, t) = 1 and u (x, 0) = x² ,y (x, t) = x + (1 – x) t² .Substitute y (x, t) = x + (1 – x) t² in equation (2),u (x, t) = v (x, t) + x + (1 – x) t² .(4)Partially differentiate both sides of the equation (4) with respect to t,ди+ 2(1 – x) tdtdtSubstitute udtdv+ 2 (1 – x) t anddx2in equation (1),dtdx2+ 5txdvdt(5)dx2When 1a², a > 0Consider the equation,v (x, t) = X (x).(6)X GET 10 FREE QUESTIONS (6),X"= -1II 2:47 PM Sat Apr 17* 8% IAAbartleby.com+X b In Problems 13-16 proceed as in Example 2 to solve the...f Facebook= bartlebyQ Search for textbooks, step-by-step explanatio...E Ask an ExpertMath / Bundle: Differential Equations with Boundary-Value P... | In Problems 13-16 proceed as in Example 2 to solve the giv...i In Problems 13-16 proceed as in Example 2 to solve the given boundary-value proble...Get live help whenever you need from online tutors! Try bartleby tutor today →DIFFERENTIALEQUATIONS withProblemsBundle: Differential Equations wit..9th EditionDennis G. ZillPublisher: Cengage LearningDENNIS G. ZILAFind 2ISBN: 9781337604901Chapter 12.6, Problem 14ETextbook ProblemIn Problems 13-16 proceed as in Example 2 to solve the given boundary-value problem.ди14.+ 2t + 3tx0 < x< 1, t> 0dx2u(0, t) = 2, u(1, t) = 1, t> 0%3Du(x, 0) = x², 0 < x<1Expert SolutionTo determineThe solution of the boundary value problem under given boundary conditions.X GET 10 FREE QUESTIONS

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