7) Obtain the solution of the following initial and boundary value problem: 4-u =03; 00, XX u(x,0) = x- 21 u(0,1)=u(r,1)=0; 0s1.
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- 2. Heat conduction in a square plate Three sides of a rectangular plate (@ = 5 m, b = 4 m) are kept at a temperature of 0 C and one side is kept at a temperature C, as shown in the figure. Determine and plot the ; temperature distribution T(x, y) in the plate. The temperature distribution, T(x, y) in the plate can be determined by solving the two-dimensional heat equation. For the given boundary conditions T(x, y) can be expressed analytically by a Fourier series (Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 1993):5. Determine the range of K for stability of the following characteristic equation, ©s(E2+s+D(s+4H)+K=0Answer the following problems;--
- I want the solution for problem 1, 2 and 3Using MATLAB, develop a computer program for the finite difference solution with general θ scheme for the 1D consolidation of a uniform layer of soil. Compare the results for θ=0, 0.5, 2/3 and 1.0 for α=0.49 and α=0.51 against the analytical solution of Terzaghi’s equation for T=0.5. Apply the program to both cases of double draining layer and single draining layer.REMARK: I need the solution for sub-question d, e ,f only
- 1. Determine the equation of the line through the given point (a) parallel and (b) perpendicular to the given line Given: Point: ( -1,-4) Line: 4x-2y=3 2. Draw the line 4x-2y=3 and your answer for letter (a) in problem number 1 3. Draw the line 4x-2=3 and your answer for letter (b) in problem number 1 4. a2x-7ay+5a=0 Reduce the given equation to (a) intercept form (b) slope-intercept form A is the last two digit of your ID number, for example your ID number 20201000111, then (a) is 11 hence your equation would be 22x-77y+55=0we have a non-linear system of differential equations: dz/dt=2z-(z^2)-zp, dp/dt=(p^2)-p(z^2) our equilibrium points are (0,0), (1,1), (2,0) and (-2,4). Write a python code that plots the phase portraits for the linearized solutions at each equilibrium point.2- Solve the following system X+y-22=3 2x+y=17 x+y-z=4
- Sir, please find me the solution for thisI'm having trouble understanding what exactly makes a linear ordinary differential equation "linear". I know that the major advantage of the linear ODEs is that a linear combination of particular solutions gives another particular solution. Characterized by additivity and homogeneity, this means that the output for a sum of inputs is equal to the sum of outputs for each individual input (e.g., f(3) + f(5) = f(3+5)= f(8)) and scaling the input by a factor scales the output by the same factor (e.g., f(6x) =6f(x)...but how would this look? Like say if I had 4e^5(t-1) satisfying the differential equation dy/dt=5y where y(1)=4, what would that "linear combination" look like?Develop a solution to calculate a student’s grade average for one semester for five courses. The lettergrades should be entered and the grade average printed out. An A is equivalent to 4 grade points, a Bis 3 grade points; a C is 2 grade points, a D is 1 grade point, and an F is zero grade points write solution in c with if else