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(3 points) In your answers below, for the variable a type the word lambda; for the...
(3 points) In your answers below, for the variable à type the word lambda; for the...
(3 points) In your answers below, for the variable à type the word lambda; for the derivative X(x) type X'; for the double derivative X(z) type X"; etc. Separate variables in the following partial differential equation for u(2,t): x?utt – (t’uz + tuzt) – z’u = 0 = • DE for X(2) • DE for T(t): =0 (Simplify your answers so that the highest derivative in each equation is positive.)
(1 point) In your answers below, for the variable i type the word lambda, for y...
(1 point) In your answers below, for the variable i type the word lambda, for y type the word gamma; otherwise treat these as you would any other variable. We will solve the heat equation u, = 4uxx: 0<x<2, 120 with boundary/initial conditions: u(0,1) = 0, and u(x,0) = So, 0<x< 1 u(2, 1) = 0, 13, 1<x<2. This models temperature in a thin rod of length L = 2 with thermal diffusivity a = 4 where the temperature at...
(7 points) Important Instructions: (1) is typed as lambda and a is typed as alpha. (2)...
(7 points) Important Instructions: (1) is typed as lambda and a is typed as alpha. (2) Use hyperbolic trig functions cosh(x) and sinh(x) instead of et and e- (3) Write the functions alphabetically, so that if the solutions involve cos and sin, your answer would be a cos(x) + b sin(x). (4) For polynomials use arbitrary constants in alphabetical order starting with lowest power of x, for example, ax + bx? (5) Write differential equations with leading term positive, so...
(7 points) Important Instructions: (1) is typed as lambda and a is typed as alpha. (2)...
(7 points) Important Instructions: (1) is typed as lambda and a is typed as alpha. (2) Use hyperbolic trig functions cosh(x) and sinh(x) instead of et and e-2. (3) Write the functions alphabetically, so that if the solutions involve cos and sin, your answer would be a cos(x) + b sin(x). (4) For polynomials use arbitrary constants in alphabetical order starting with lowest power of x, for example, ax + bx2. (5) Write differential equations with leading term positive, so...
(2 points) is typed as lambda, a as alpha. The PDE a2u ar2 = yº ди...
(2 points) is typed as lambda, a as alpha. The PDE a2u ar2 = yº ди ay is separable, so we look for solutions of the form u(x, t) = X(x)Y(y). When solving DE in X and Y use the constants a and b for X and c for Y. The PDE can be rewritten using this solution as (placing constants in the DE for Y) into X"/X (1/(k^2))(y^5)(Y'/Y) = -2 Note: Use the prime notation for derivatives, so the...
Please only fill in the red blanks (2 points) is typed as lambda, a as alpha....
Please only fill in the red blanks
(2 points) is typed as lambda, a as alpha. The PDE yº au au ar ay is separable, so we look for solutions of the form u(x, t) = X(2)Y(y). When solving DE in X and Y use the constants a and b for X and c for Y. The PDE can be rewritten using this solution as (placing constants in the DE for Y) into X"/X = (1/(k^2))(y^5)(Y'/Y) -2 Note: Use the...
% 5.4.29 :3 Question Help Find the critical points and solve the related phase plane differential...
% 5.4.29 :3 Question Help Find the critical points and solve the related phase plane differential equation for the system below. df = (x – 4)(y-4) d = y(y-4) Describe (without using computer software) the asymptotic behavior of trajectories (as t → 00) that start at (a) (5,5), (b) (7.5),(6)(-7.5),(a) (-5,-5). choice. A. The critical points lie along the line(s) y=4 and also occur at the point(s) (4,0). (Type an equation. Type an ordered pair. Use a comma to separate...
4. (50 pts) Consider the following partial differential equation: 1du au Ət22 Ətər2 (BC) u7,t) =...
4. (50 pts) Consider the following partial differential equation: 1du au Ət22 Ətər2 (BC) u7,t) = 0 20,t) = 0 0 <t (IC) u(3,0) = 0 0 <r <a Follow the steps below to solve it: (a) (8 pts) Separate variables as u(x,t) = X(2)T(t) to derive the following differential equations for X and T, with an unknown parameter 1: T" - T' + XT = 0, X" + 1X = 0.
tal Question 3 Find each of the following. Explanations/working need to be provided to earn full marks. 3(a). Const...
tal Question 3 Find each of the following. Explanations/working need to be provided to earn full marks. 3(a). Construct the Euler-method algorithm for the differential equation y(t) (1+1) sin y(t) (i.e., how do you determine yn +1 HO fron yn?). 7 = b). Compute the partial derivative , if w o(u,u) = uv, where the (u, u)variables are defined by u(z, y-r2+Sy2 and v(x, y) = 2r2-f
tal Question 3 Find each of the following. Explanations/working need to be provided...
We can apply the Method of Separation of Variables to obtain a representation for the solution u ...
Please show all work and provide and an original solution.
We can apply the Method of Separation of Variables to obtain a representation for the solution u u(, t) for the following partial differential equation (PDE) on a bounded domain with homogeneous boundary conditions. The PDE model is given by: u(r, 0) 0, (2,0) = 4. u(0,t)0, t 0 t 0 (a) (20 points) Assume that the solution to this PDE model has the form u(x,t) -X (r) T(t). State...
(3 points) In your answers below, for the variable à type the word lambda; for the derivative X(x) type X'; for the double derivative X(z) type X"; etc. Separate variables in the following partial differential equation for u(2,t): x?utt – (t’uz + tuzt) – z’u = 0 = • DE for X(2) • DE for T(t): =0 (Simplify your answers so that the highest derivative in each equation is positive.)
(1 point) In your answers below, for the variable i type the word lambda, for y type the word gamma; otherwise treat these as you would any other variable. We will solve the heat equation u, = 4uxx: 0<x<2, 120 with boundary/initial conditions: u(0,1) = 0, and u(x,0) = So, 0<x< 1 u(2, 1) = 0, 13, 1<x<2. This models temperature in a thin rod of length L = 2 with thermal diffusivity a = 4 where the temperature at...
(7 points) Important Instructions: (1) is typed as lambda and a is typed as alpha. (2) Use hyperbolic trig functions cosh(x) and sinh(x) instead of et and e- (3) Write the functions alphabetically, so that if the solutions involve cos and sin, your answer would be a cos(x) + b sin(x). (4) For polynomials use arbitrary constants in alphabetical order starting with lowest power of x, for example, ax + bx? (5) Write differential equations with leading term positive, so...
(7 points) Important Instructions: (1) is typed as lambda and a is typed as alpha. (2) Use hyperbolic trig functions cosh(x) and sinh(x) instead of et and e-2. (3) Write the functions alphabetically, so that if the solutions involve cos and sin, your answer would be a cos(x) + b sin(x). (4) For polynomials use arbitrary constants in alphabetical order starting with lowest power of x, for example, ax + bx2. (5) Write differential equations with leading term positive, so...
(2 points) is typed as lambda, a as alpha. The PDE a2u ar2 = yº ди ay is separable, so we look for solutions of the form u(x, t) = X(x)Y(y). When solving DE in X and Y use the constants a and b for X and c for Y. The PDE can be rewritten using this solution as (placing constants in the DE for Y) into X"/X (1/(k^2))(y^5)(Y'/Y) = -2 Note: Use the prime notation for derivatives, so the...
Please only fill in the red blanks
(2 points) is typed as lambda, a as alpha. The PDE yº au au ar ay is separable, so we look for solutions of the form u(x, t) = X(2)Y(y). When solving DE in X and Y use the constants a and b for X and c for Y. The PDE can be rewritten using this solution as (placing constants in the DE for Y) into X"/X = (1/(k^2))(y^5)(Y'/Y) -2 Note: Use the...
% 5.4.29 :3 Question Help Find the critical points and solve the related phase plane differential equation for the system below. df = (x – 4)(y-4) d = y(y-4) Describe (without using computer software) the asymptotic behavior of trajectories (as t → 00) that start at (a) (5,5), (b) (7.5),(6)(-7.5),(a) (-5,-5). choice. A. The critical points lie along the line(s) y=4 and also occur at the point(s) (4,0). (Type an equation. Type an ordered pair. Use a comma to separate...
4. (50 pts) Consider the following partial differential equation: 1du au Ət22 Ətər2 (BC) u7,t) = 0 20,t) = 0 0 <t (IC) u(3,0) = 0 0 <r <a Follow the steps below to solve it: (a) (8 pts) Separate variables as u(x,t) = X(2)T(t) to derive the following differential equations for X and T, with an unknown parameter 1: T" - T' + XT = 0, X" + 1X = 0.
tal Question 3 Find each of the following. Explanations/working need to be provided to earn full marks. 3(a). Construct the Euler-method algorithm for the differential equation y(t) (1+1) sin y(t) (i.e., how do you determine yn +1 HO fron yn?). 7 = b). Compute the partial derivative , if w o(u,u) = uv, where the (u, u)variables are defined by u(z, y-r2+Sy2 and v(x, y) = 2r2-f
tal Question 3 Find each of the following. Explanations/working need to be provided...
Please show all work and provide and an original solution.
We can apply the Method of Separation of Variables to obtain a representation for the solution u u(, t) for the following partial differential equation (PDE) on a bounded domain with homogeneous boundary conditions. The PDE model is given by: u(r, 0) 0, (2,0) = 4. u(0,t)0, t 0 t 0 (a) (20 points) Assume that the solution to this PDE model has the form u(x,t) -X (r) T(t). State...
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