both give the same result. both the d'Alembert solution and the separation of variables method and show that Solve the wave equation d'u1du dr ar %3D ject to the initial conditions (a) utx, 0) = sin.x (all x) du (x, 0) = 0 (b) 3t (all x) both give the same result.
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- Caculate both Parts a) y''-2y'-3y=x+1 b) y''+4y=sin3xSolve the inhomogeneous wave equation on the real lineUtt − c2Uxx = sin x, x ∈ RU(x, 0) = 0, Ut(x, 0) = 0.Explain what theory you are using and show your full computations.Find the solution of the wave equation when initial velocity equal to 0 and initial deflection is (2kx/l) when x between zero and (1/2) and deflection equal to (2k(l-x)/I) when x between (1/2) and (I) the P.D.E. is * c2 dx²
- Select the wave equation by utilizing separate variables with initial conditions?Show that the function Z = sin(wct)sin(wx) satisfies the wave equationFind the location at t = 3 of a particle whose path satisfies dr = (181-1712-21-4) dt + r(0) = (8,7) (Use symbolic notation and fractions where needed. Give your answer in vector form.) r(3) = (54,4) Incorrect
- The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the vector function 7(t) = 3(10t – sin(10t))ỉ + 3(1 – cos(104))} Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) Find the speed of the point. s(t) =DON'T USE CHATGPT Solve the following equation by canceling operator y"+y = 3x sin(x) (In the answer instead of the constants put A and B instead of C_1 and C_2)Eliminate the arbitrary constant a from the equation (z - a) + y = a° O = + 2ryy" O = + 2ry' Ov =r+ 2ryy O-r+ 2ry'
- The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the vector function 7(t) = 3(22t – sin(22t))i + 3(1 – cos(22t))} Find the velocity vector of the point. v(t) = (66 – 66 cos(22t) )i + 66 sin( 22t)jv Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t) = 66y cos( 22t) + sin( 22t) xFind the approximation for the Green's function of the one-dimensional acoustic wave equation in the case where velocity is given by: c(x) = aebx , where a and b are real numbers and a > 0. Analyze each case, b 0, in detail.How do I parametrize to get r1(x) and r2(x).