Please show all work and answer all parts with an original solution.
Please show all work and answer all parts with an original solution. Find the solution rt)...
Locate the solution region Find the corners. (Select all that apply.) (0, 5/2) (0, 2) (0, 5) (0, 6) (1, 2) (1, 3) (5/3, 0) (2,1) (3,1) (5,0) (6,0) The graph of the boundary equations for the system of inequalities is shown with the system. 2x + 6y 2 12 3x + 6y > 15 6x + 2y > 10 x20, y20 6x + 2y = 10 3x + y = 15 2x + y = 12
PROBLEM 1 IS SUPPOSED TO BE A WAVE EQUATION NOT HEAT EQUATION 1. Find the solution to the following boundary value initial value problem for the Heat Equation au 22u 22 = 22+ 2 0<x<1, c=1 <3 <1, C u(0,t) = 0 u(1,t) = 0 (L = 1) u(x,0) = f(x) = 3 sin(7x) + 2 sin (3x) (initial conditions) (2,0) = g(x) = sin(2x) 2. Find the solution to the following boundary value problem on the rectangle 0 <...
4. (10 points) Find the solution to the wave problem Ut = c+421 +COSI, <0, t>0, with initial conditions u(1,0) = sin r, 4(1,0) = 1+I.
4. [10] Find the solution to given initial-boundary value problem: 4uxx = ut 0<x<TI, t> 0 u(0,t) = 5, uit, t) = 10, t> 0 u(x,0) = sin 3x - sin 5x, 0<x<T
4. Consider the boundary value problem defined by the partial differential equation д?и д?и = 0, ду? y > 0, да? with boundary conditions u(0, y) = u(T,y) = 0, u(x, 0) = 1 and limy-v00 |u(x, y)|< 0o. (a) Use separation of variables to find the eigenvalues and general series solution in terms of the normal modes. (b) Impose the inhomogeneous boundary condition u(x,0) = 1 to find the constants in the general series solution and hence the solution...
Question 1 - 16 Consider the following intial-boundary value problem. au au 0<x< 1, 10, at2 ax?' u(0,t) = u(11,t) = 0, 7>0, u(x,0) = 1, 34(x,0) = sin10x + 7sin50x. (show all your works). A) Find the two ordinary differential equations (ODES). B) Solve these two ODES. Show all cases 1 <0, 1 = 0, and > 0 C) Write the complete solution of this initial - boundary value problem.
Let u be the solution to the initial boundary value problem for the Heat Equation, фа(t, x)-5 &n(t, x), t E (0,00), x E (0, 1); with initial condition 2 r-, 1 and with boundary condition:s n(t, 0)=0, rn(t, 1-0. Find the solution u using the expansion with the normalization conditions vn (0)-1, wn a. (3/10) Find the functions wz, with indexn> 1 b. (3/10) Find the functions v, with index n> 1. c. (4/10) Find the coefficients cn, with...
4.[10] Find the solution to given initial-boundary value problem: 4uxx = U, 0 < x <TT, t> 0 u(0,t) = 5, u(t, t) = 10, t> 0 u(x,0) = = sin 3x - sin 5x, 0<x<
Please help, I will rate for your answer 3. Use the Maximum/Minimum Principles to deduce that the solution u of the problem D.E. u = kuv 0 < x < 1, t > 0. B.C. u(0,0) = 0 (7,t) = 0 I.C. u(x,0) = sin(x) + {sin(2x) satisfies 0 < u(x,t) < 3/3/4 for all OSXST, 120.
Just need the answer and no steps. The solution of the heat equation Uxx = U7, 0 < x < 2,1 > 0, which satisfies the boundary conditions u(0, t) = u(2,t) = 0 and the initial condition u(x, 0) = f(x), (1, 0 < x < 1 L where f(x) = 3 }, is u(x, t) = į bn sin (n7x De 7 ,where bn = 10,1 < x < 2 S n=1 Select one: o a [(-1)] o...