3.1.4. Find all separable eigensolutions to the following partial differential equations: (b) ut = ux (c)...
3.1.4. Find all separable eigensolutions to the following
partial differential equations:
(b) ut = ux
(c) ut = xux.
Homework Answers
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3.1.4. Find all separable eigensolutions to the following
partial differential equations:
(b) ut = ux
(c)...
please show all steps 4. Some equations that are not separable can be made separable by...
please show all steps
4. Some equations that are not separable can be made separable by an appropriate substitution. Differential equations of the form y = f (!) are called Euler-homogeneous. These can be solved by letting v = y/t or y = ut. Using the product rule, dy du di = v + tai so that the differential equation becomes du v+t du f(0) - 0 dt t Use this technique to solve dy 2y+ + +4 - Leave...
We use the last two Maxwell's Equations to derive the following two partial differential equations Use...
We use the last two Maxwell's Equations to derive the following two partial differential equations Use the above equations and the traveling wave equations for electric and magnetic field (E-Em Sin (Kx-ut) and B = B-Sin (Kx-ut) To prove speed of light formula C-1???.
Question 14 (12 marks) Consider the following separable differential equation. dy cos(z)(-1) dr (a) Find any...
Question 14 (12 marks) Consider the following separable differential equation. dy cos(z)(-1) dr (a) Find any constant solutions of this differential equation and hence write down the solution with initial value y=- when r=7 (b) Use partial fractions to evaluate 1 dy. 1 (c) Use the method for solving separable differential equations to solve this DE in the case where y 0 when r T. You may assume that the solution does not cross the constant solutions you found in...
1 & 5 Solve the following heat equations using Fourier series ux Ut, 0 <x <1,t>0,...
1 & 5
Solve the following heat equations using Fourier series ux Ut, 0 <x <1,t>0, u (0,t) = 0 = u(1,t), u(x,0) = x/2 1/ 2/ Ux=Ut, 0<x< m ,t>0 ,u(0,t) = 0 = u( 1, t), u(x, O) = sinx- sin3x 3/ usxut, O <x < 1 ,t>0, u(0,t) = 0 = u,(1, t), u(x,0) = 1 -x2 Ux=Ut,O<x <m ,t>0, u(0, t) = 0 = u,( rt , t) , u(x, 0) = (sinxcosx)2 4/ 5/Solve the...
Find the general solutions (implicitly if necessary, explicitly if convenient) of the separable differential equations. dy/dx...
Find the general solutions (implicitly if necessary, explicitly if convenient) of the separable differential equations. dy/dx = ysinx
QUESTION 2 Which of the following differential equations is separable? ︵ v'-e"sin(xy) QUESTION 2 Whic...
QUESTION 2 Which of the following differential equations is separable? ︵ v'-e"sin(xy)
QUESTION 2 Which of the following differential equations is separable? ︵ v'-e"sin(xy)
6. (3 points) Classify each of the following differential equations as separable, linear, both, or neither....
6. (3 points) Classify each of the following differential equations as separable, linear, both, or neither. (b) 3y - + Gary - 2 (c) V+zyme
for differential equations 1. Identify each of the following differential equations as either Separable, Homogeneous, Linear...
for
differential equations
1. Identify each of the following differential equations as either Separable, Homogeneous, Linear Bernoulli, or Exact and solve the equation using the method of the type you have identified. Many can be classified in multiple ways, it is not necessary to list all possibilities. (3xy2 +2ycos x)+y'-y sin x-x =0 Туре: A. dx General Solution: B. (4xy+xy)2x+ xy2 dx Туре: General Solution: Туре: C. y'y'y+1 General Solution: (3x'y+e')-(2y-x-xe)dy Туре: D. dx General Solution: Туре: dy E. =y(xy-1)...
partial differential equations question Problem 6. a) Find all possible surfaces orthogonal to the planes x...
partial differential equations question
Problem 6. a) Find all possible surfaces orthogonal to the planes x + 2y + cz = 1, where c is an arbitrary real constant. (b) Find the surface orthogonal to the planes x+2y+cz = 1 passing through the curve I: x = s, y = s, z = sa.
Partial Differential Equations Question: A homogeneous cylindrical rod of length L = 1 is insulated along...
Partial Differential Equations Question: A homogeneous cylindrical rod of length L = 1 is insulated along the cylindrical side. At the end caps, heat exchange obeys Newton’s law of cooling, i.e. the flux is proportional to the difference of the temperature of the rod with that of the surrounding medium, written explicitly as ux(0,t) = u(0,t ) -T1 and ux(1,t) = T2- u(1,t) where T1 = 0 and T2 = 1. Find the steady state distribution of the temperature.
please show all steps
4. Some equations that are not separable can be made separable by an appropriate substitution. Differential equations of the form y = f (!) are called Euler-homogeneous. These can be solved by letting v = y/t or y = ut. Using the product rule, dy du di = v + tai so that the differential equation becomes du v+t du f(0) - 0 dt t Use this technique to solve dy 2y+ + +4 - Leave...
We use the last two Maxwell's Equations to derive the following two partial differential equations Use the above equations and the traveling wave equations for electric and magnetic field (E-Em Sin (Kx-ut) and B = B-Sin (Kx-ut) To prove speed of light formula C-1???.
Question 14 (12 marks) Consider the following separable differential equation. dy cos(z)(-1) dr (a) Find any constant solutions of this differential equation and hence write down the solution with initial value y=- when r=7 (b) Use partial fractions to evaluate 1 dy. 1 (c) Use the method for solving separable differential equations to solve this DE in the case where y 0 when r T. You may assume that the solution does not cross the constant solutions you found in...
1 & 5
Solve the following heat equations using Fourier series ux Ut, 0 <x <1,t>0, u (0,t) = 0 = u(1,t), u(x,0) = x/2 1/ 2/ Ux=Ut, 0<x< m ,t>0 ,u(0,t) = 0 = u( 1, t), u(x, O) = sinx- sin3x 3/ usxut, O <x < 1 ,t>0, u(0,t) = 0 = u,(1, t), u(x,0) = 1 -x2 Ux=Ut,O<x <m ,t>0, u(0, t) = 0 = u,( rt , t) , u(x, 0) = (sinxcosx)2 4/ 5/Solve the...
QUESTION 2 Which of the following differential equations is separable? ︵ v'-e"sin(xy)
QUESTION 2 Which of the following differential equations is separable? ︵ v'-e"sin(xy)
6. (3 points) Classify each of the following differential equations as separable, linear, both, or neither. (b) 3y - + Gary - 2 (c) V+zyme
for
differential equations
1. Identify each of the following differential equations as either Separable, Homogeneous, Linear Bernoulli, or Exact and solve the equation using the method of the type you have identified. Many can be classified in multiple ways, it is not necessary to list all possibilities. (3xy2 +2ycos x)+y'-y sin x-x =0 Туре: A. dx General Solution: B. (4xy+xy)2x+ xy2 dx Туре: General Solution: Туре: C. y'y'y+1 General Solution: (3x'y+e')-(2y-x-xe)dy Туре: D. dx General Solution: Туре: dy E. =y(xy-1)...
partial differential equations question
Problem 6. a) Find all possible surfaces orthogonal to the planes x + 2y + cz = 1, where c is an arbitrary real constant. (b) Find the surface orthogonal to the planes x+2y+cz = 1 passing through the curve I: x = s, y = s, z = sa.
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