Question

In: Advanced Math

Solve the initial value problem Utt = c^2Uxx, u(0,x)= e^-x^2 , Ut(0,x) = sin x (PDE)

Solve the initial value problem Utt = c^2Uxx,

u(0,x)= e^-x^2 , Ut(0,x) = sin x

(PDE)

Solutions

Expert Solution


Related Solutions

Suppose u(t,x)solves the initial value problem Utt = 4Uxx + sin(wt) cos(x), u(0,x)= 0 , Ut(0,x)...
Suppose u(t,x)solves the initial value problem Utt = 4Uxx + sin(wt) cos(x), u(0,x)= 0 , Ut(0,x) = 0. Is h(t) = u(t,0) a periodic function? (PDE)
Solve the Boundary Value Problem, PDE: Utt-a2uxx=0, 0≤x≤1, 0≤t<∞ BCs: u(0,t)=0 u(1,t)=cos(t) u(x,0)=0 ut(x,0)=0
Solve the Boundary Value Problem, PDE: Utt-a2uxx=0, 0≤x≤1, 0≤t<∞ BCs: u(0,t)=0 u(1,t)=cos(t) u(x,0)=0 ut(x,0)=0
Solve the following initial value problem ut + 2ux − 2u = e t+2x , u(x,...
Solve the following initial value problem ut + 2ux − 2u = e t+2x , u(x, 0) = 0
Find the unique solution u of the parabolic boundary value problem Ut −Uxx =e^(−t)*sin(3x), 0<x<π, t>0,...
Find the unique solution u of the parabolic boundary value problem Ut −Uxx =e^(−t)*sin(3x), 0<x<π, t>0, U(0,t) = U(π,t) = 0, t > 0, U(x, 0) = e^(π), 0 ≤ x ≤ π.
Solve the following initial value problems: a) ut+xux= -tu, x is in R, t>0; u(x,0) =f(x),...
Solve the following initial value problems: a) ut+xux= -tu, x is in R, t>0; u(x,0) =f(x), x is in R. c) ut+ux=-tu, x is in R, t>0; u(x,0)=f(x), x is in R d)2ut+ux = -2u, x,t in R, t>0; u(x,t)=f(x,t) on the straight line x = t, where f is a given function.
Solve the initial value problem dy/dx = −(2x cos(x^2))y + 6(x^2)e^(− sin(x^2)) , y(0) = −5...
Solve the initial value problem dy/dx = −(2x cos(x^2))y + 6(x^2)e^(− sin(x^2)) , y(0) = −5 Solve the initial value problem dy/dt = (6t^5/(1 + t^6))y + 7(1 + t^6)^2 , y(1) = 8. Find the general solution of dy/dt = (2/t)*y + 3t^2* cos3t
(PDE) Find the series soln to Ut=Uxx on -2<x<2, T>0 with Dirichlet boundary { U(t,-2)=0=U(t, 2)...
(PDE) Find the series soln to Ut=Uxx on -2<x<2, T>0 with Dirichlet boundary { U(t,-2)=0=U(t, 2) initial condition { U(0,x) = { x, IxI <1
Find the finite-difference solution of the heat-conduction problem PDE: ut = uxx 0 < x <...
Find the finite-difference solution of the heat-conduction problem PDE: ut = uxx 0 < x < 1, 0 < t < 1 BCs: ⇢ u(0, t) = 0 ux(1, t) = 0 0 < t < 1 IC: u(x, 0) = sin(pi x) 0 x  1 for t = 0.005, 0.010, 0.015 by the explicit method. Assume
For the wave equation, utt = c2uxx, with the following boundary and initial conditions, u(x, 0)...
For the wave equation, utt = c2uxx, with the following boundary and initial conditions, u(x, 0) = 0 ut(x, 0) = 0.1x(π − x) u(0,t) = u(π,t) = 0 (a) Solve the problem using the separation of variables. (b) Solve the problem using D’Alembert’s solution. Hint: I would suggest doing an odd expansion of ut(x,0) first; the final solution should be exactly like the one in (a).
Solve the initial value problem: y''+2y'+y = x^2 , y(0)=0 , y'(0) = 0
Solve the initial value problem: y''+2y'+y = x^2 , y(0)=0 , y'(0) = 0
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT