1 answer

3. (5 points). Find the solution urt) of the equation 4 = Urur, subject to the...

Question:

3. (5 points). Find the solution urt) of the equation 4 = Urur, subject to the boundary conditions (0,t) = 1, u(2, 1) = 3, an

3. (5 points). Find the solution urt) of the equation 4 = Urur, subject to the boundary conditions (0,t) = 1, u(2, 1) = 3, and the initial condition u(x,0) = 3.2 +1.

Answers

Solution ut Uxx Boundary a b (c * Note: [c, cospa + C, simpx]. Ca è breat ulo,t) = C, C3 è p²t given, conditions: ulo, ut ) =(C, cosap + C₂ sin p). Cze-p²t. Solving e 6 C, Cz ébet - 1 4 ) ci) = 3 On { i) in using we get, C2=C, (3-cosap) wis} C3 = क eNow the general solution is {an cos(91+ )x+ bn sin (n***) 3. emazs ula,t) = n=1 where anc, C₃ & bn=c₂ C3 there с using u(a,0)

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