Can anyone help with this question please? Any help will be appreciated!!!
Can anyone help with this question please? Any help will be appreciated!!! Consider a general first order equation of t...
Can anyone help with this question please? The initial boundary condition is trivial, I struggled to show the first condition. Any help will be appreciated!!! Let now Ω c Rd be an open and bounded set with a smooth boundary on and outer unit normal n. Furthermore, let f : Ω → R be a continuous function. Define the functional where weg-(u E C10) |v = 0 and ▽u . n = 0 in 201. Show that a minimiser u...
please provide me with full working solution. Any help is appreciated. thank you in advance Consider the diffusion equation, au(x,t u(x,t) Here u(x,t) > 0 is the concentration of some diffusing substance, the spatial variable is x, time is t and D is a constant called the diffusivity with dimensions [LT-11. We will consider the diffusion equation on a finite spatial domain (0<x< 1) and an infinite time horizon (t > 0). To solve the diffusion equation we must include...
Can anyone help with this question please? Given a domain Ω c R2 and a smooth function f,uo : Ω-+ R consider the problem Uz (x, t)-Au (x, t) + u(x, t) u(x, t = f(x) Y(x, t) E Ω × (0, oo), V(x, t) E 2 x (0, 00), Assume that u(z, t) is a smooth solution and that v(x) is a smooth stationary (i.e., time-independent) solution. Derive a PDE problem for the difference w(x, t)u(x, t)(x) By multiplying...
Consider the first order separable equation y(1 + 53*) 1/3 An implicit general solution can be written in the form yCf(x) for some function f(x) with an arbitrary constant. Here f(x) Next find the explicit solution of the initial value problem y(0) = 3 y =
(1 point) Consider the first order separable equation y = 16xy(1+2x51/3 An Implicit general solution can be written in the form y = Cf(x) for some function f(x) with C an arbitrary constant. Here f(x) e (1+2x^6)^(4/3) Next find the explicit solution of the initial value problem y(0) = 5
(1 point) Consider the first order separable equation y' y(y- 1) An implicit general solution can be written in the form e + h(x, y) Find an explicit solution of the initial value problem y(0)3 C where h(z, y) ( y)
sef (1 point) Consider the first order separable equation y' = 45x®y(1 +520)1/2 An explicit general solution can be written in the form y=Cf(x) for some function f(x) with Can arbitrary constant. Here f(x) = Next find the explicit solution of the initial value problem y(0) = 1 y=
A9.5.36 Question Help Find a general solution to the system below. -2 x(t) x'(t) = This system has a repeated eigenvalue and one linearly independent eigenvector. To find a general solution, first obtain a nontrivial solution x, (t). Then, to obtain a second linearly independent solution, try x2 (t) = te"u, + e"u2, where r is the eigenvalue of the matrix and u, is a corresponding eigenvector. Use the equation (A - rl)u, = u, to find the vector u,....
I need help with d) please help thank you Question 1 Wave motion appears in all branches of physics. In the lectures we considered the solution of the advection equation, a first-order hyperbolic PDE. Here we consider the solution of the wave equation: c2 where c >0 is constant. , We assume all variables have been non-dimensionalised. (a) Eq. (1) has the general solution (d'Alembert, 1747): u(x,t) F(x -ct) +G(x ct), where F and G are arbitrary functions. Consider the...
Question 2 Consider the differential equation We saw in class that one solution is the Bessel function (a) Suppose we have a solution to this ODE in the form y-Σχ0CnXntr where cn 0. By considering the first term of this series show that r must satisfy r2-4-0 (and hence that r = 2 or r =-2) (b) Show that any solution of the form y-ca:0G,2n-2 must satisfy C0 (c) From the theory about singular solutions we know that a linearly...