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(1 point) In your answers below, for the variable i type the word lambda, for y...
(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.)
(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...
(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 this problem we find the eigenfunctions and eigenvalues of the differential equation B+...
(1 point) In this problem we find the eigenfunctions and eigenvalues of the differential equation B+ iy=0 with boundary conditions (0) + (0) = 0 W2) = 0 For the general solution of the differential equation in the following cases use A and B for your constants, for example y = A cos(x) + B sin(x)For the variable i type the word lambda, otherwise treat it as you would any other variable. Case 1: 1 = 0 (1a.) Ignoring the...
(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...
solve the PDE +u= at2 on 3 € (0,L), t > 0, with boundary conditions au...
solve the PDE
+u= at2 on 3 € (0,L), t > 0, with boundary conditions au 2x2 u(0,t) = 0, u(L, t) = 0 au and initial condition u(x,0) = f(x), at (x,0) = g(x) following the steps below. (a) Separate the variables and write differential equations for the functions (x) and h(t); pick the separation constant so that we recover a problem already studied. (b) Find the eigenfunctions and eigenvalues. (c) Write the general solution for this problem. (d)...
(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...
A rectangular lamina of width a and height b is sandwiched between two slabs of ice, so that the lower and upper sides, of width a, are at a temperature Θ 0, The other two sides are thermally isolat...
A rectangular lamina of width a and height b is sandwiched between two slabs of ice, so that the lower and upper sides, of width a, are at a temperature Θ 0, The other two sides are thermally isolated. Fix coordinates so that the origin below is the lower left corner, as shown in the figure се се Model this situation as a temperature e(x, y,t) that satisfies the two-dimensional diffusion equation with thermal diffusivity D, namely ot together with...
This is a partial differential equations question. Please help me solve for u(x,t): Find the eigenvalues/eigenfunction...
This is a partial differential equations question. Please help
me solve for u(x,t):
Find the eigenvalues/eigenfunction and then use the initial
conditions/boundary conditions to find Fourier coefficients for the
equation.
3. (10 pts) Use the method of separating variables to solve the problem utt = curr u(0,t) = 0 = u(l,t) ur. 0) = 3.7 - 4, u(3,0) = 0 for 0 <r<l, t>0 fort > 0 for 0 <r<1
(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.)
(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...
(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 this problem we find the eigenfunctions and eigenvalues of the differential equation B+ iy=0 with boundary conditions (0) + (0) = 0 W2) = 0 For the general solution of the differential equation in the following cases use A and B for your constants, for example y = A cos(x) + B sin(x)For the variable i type the word lambda, otherwise treat it as you would any other variable. Case 1: 1 = 0 (1a.) Ignoring the...
(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...
solve the PDE
+u= at2 on 3 € (0,L), t > 0, with boundary conditions au 2x2 u(0,t) = 0, u(L, t) = 0 au and initial condition u(x,0) = f(x), at (x,0) = g(x) following the steps below. (a) Separate the variables and write differential equations for the functions (x) and h(t); pick the separation constant so that we recover a problem already studied. (b) Find the eigenfunctions and eigenvalues. (c) Write the general solution for this problem. (d)...
(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...
A rectangular lamina of width a and height b is sandwiched between two slabs of ice, so that the lower and upper sides, of width a, are at a temperature Θ 0, The other two sides are thermally isolated. Fix coordinates so that the origin below is the lower left corner, as shown in the figure се се Model this situation as a temperature e(x, y,t) that satisfies the two-dimensional diffusion equation with thermal diffusivity D, namely ot together with...
This is a partial differential equations question. Please help
me solve for u(x,t):
Find the eigenvalues/eigenfunction and then use the initial
conditions/boundary conditions to find Fourier coefficients for the
equation.
3. (10 pts) Use the method of separating variables to solve the problem utt = curr u(0,t) = 0 = u(l,t) ur. 0) = 3.7 - 4, u(3,0) = 0 for 0 <r<l, t>0 fort > 0 for 0 <r<1
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