Prove that the functions (a)
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Numerical Analysis
- Consider the family of functions uc(x,t) of two variables x,t, indexed by the parameter c,uc(x,y)=ln(x+ct)(cos(ct)cos(x)−sen(ct)sin(x)).Determine the value of the parameter c>0 so that the function uc(x,y) is a solution of the wave equationarrow_forwardVerify that the function u(x, t) = (r – at)° + (x + at)° satisfies the wave equation uu =arrow_forward11) Calculate the Jacobian, J, for the change of variables x = u cos(e) - v sin(e) and y = u sin(0) + v cos(0).arrow_forward
- - 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) – v sin(0) and yu sin(0) + v cos(0).arrow_forward2. Suppose that a motion described by the vector valued function (i.e. position function) r(t) has velocity given by r'(t) = v(t) = (5 cos t, 5 sin t, –2) and that r(0.) = (2,1, 1). Find the formula for the position function r(t).arrow_forwardShow that the function a(z, t) = bi sin )cos() + b sin cos( 2) Tct 2nct bị sin COS L + b2 sin L COS L where c, L, b1, b2 are nonzero constants with L > 0 and c > 0, is a solution to the one-dimensional wave equation c2.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage