Homework Answers
Put u(x,t) = X(x).T(t) in given PDE and the separate the variables X and T.
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(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 a type the word lambda; for the...
(3 points) In your answers below, for the variable a type the word lambda; for the derivative x(x) type X'; for the double derivative X(x) type X"'; etc. d? dx2 Separate variables in the following partial differential equation for u(x, t): tuz – tuxt + x²u1 + x?u= 0 = = a -
(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...
what are the solutions? pls box answers Η Αμμ5 e Laredo College PA... 3 Microsoft Word...
what are the solutions? pls box answers
Η Αμμ5 e Laredo College PA... 3 Microsoft Word - I... MATH 1314.EP1 College Algebra S.S. 1 Online 2020 Homework: Quiz 8.2 Systems of Linear Equations: Matrices Score: 0 of 1 pt 10 of 15 (10 complete) X 8.2.49 Solve the following system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent x - y = 6 3x - 2z = 21 3y + 5z...
(1 point) For partial derivatives of a function use the subscript notation, so for the second par...
(1 point) For partial derivatives of a function use the subscript notation, so for the second partial derivative of the function u(x,t) with respect to x use uxx. For ordinary differential equations use the prime notation, so the second derivative of the function f(x) is f" Solve the heat equation 14 1502,>0 a(0,t) = 92,21(2, t) 87, t > 0 using a steady-state and transient solution: ie write u(z, 1) _ u(z,t) + S(z) with u a solution of the...
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...
3. In the problems below, you may use the formal solution of the appropriate partial differential...
3. In the problems below, you may use the formal solution of the appropriate partial differential equation and boundary conditions from course notes and the text. You do not have to derive the formal solution. (a) (15 points) Find the solution of the initial-boundary value problem du du ət – Ər2 t> 0, 0 < x <7, u(0,t) = , t>0, u( ,t) = 0, t>0, u(x,0) = sin 2x, 0<x< 7. (b) (10 points) Solve the initial-boundary value problem...
(3 points) In your answers below, for the variable a type the word lambda; for the derivative x(x) type X'; for the double derivative X(x) type X"'; etc. d? dx2 Separate variables in the following partial differential equation for u(x, t): tuz – tuxt + x²u1 + x?u= 0 = = a -
(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...
what are the solutions? pls box answers
Η Αμμ5 e Laredo College PA... 3 Microsoft Word - I... MATH 1314.EP1 College Algebra S.S. 1 Online 2020 Homework: Quiz 8.2 Systems of Linear Equations: Matrices Score: 0 of 1 pt 10 of 15 (10 complete) X 8.2.49 Solve the following system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent x - y = 6 3x - 2z = 21 3y + 5z...
(1 point) For partial derivatives of a function use the subscript notation, so for the second partial derivative of the function u(x,t) with respect to x use uxx. For ordinary differential equations use the prime notation, so the second derivative of the function f(x) is f" Solve the heat equation 14 1502,>0 a(0,t) = 92,21(2, t) 87, t > 0 using a steady-state and transient solution: ie write u(z, 1) _ u(z,t) + S(z) with u a solution of the...
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...
3. In the problems below, you may use the formal solution of the appropriate partial differential equation and boundary conditions from course notes and the text. You do not have to derive the formal solution. (a) (15 points) Find the solution of the initial-boundary value problem du du ət – Ər2 t> 0, 0 < x <7, u(0,t) = , t>0, u( ,t) = 0, t>0, u(x,0) = sin 2x, 0<x< 7. (b) (10 points) Solve the initial-boundary value problem...
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