Question

Solve the non homogenous wave equation , Utt - c^2Uxx =1 ,

u(x,0) = sin (x) , Ut(x,0) = 1+x

(PDE)

Answer #1

Solve the wave equation Utt - C^2 Uxx = 0 with initial condtions
:
1) u(x,0) = log (1+x^2), Ut(x,0) = 4+x
2) U(x,0) = x^3 , Ut(x,0) =sinx
(PDE)

Solve the wave equation:
utt = c2uxx, 0<x<pi, t>0
u(0,t)=0, u(pi,t)=0, t>0
u(x,0) = sinx, ut(x,0) = sin2x, 0<x<pi

Solve the following wave equation using Fourier Series
a2uxx = utt, 0 < x < pi,
t > 0, u(0,t) = 0 = u(pi,t), u(x,0) = sin2x - sin3x,
ut(x,0) = 0

Solve the following wave equation using Fourier Series
a2uxx = utt, 0 < x < pi,
t > 0, u(0,t) = 0 = u(pi,t), u(x,0) = sinxcosx,
ut(x,0) = x(pi - x)

Solve the following wave equation using Fourier Series
a2uxx = utt, 0 < x < L, t
> 0, u(0,t) = 0 = u(L,t), u(x,0) = x(L - x)2,
ut(x,0) = 0

8. Find the solution of the following PDE:
utt − 9uxx = 0
u(0, t) = u(3π, t) = 0
u(x, 0) = sin(x/3)
ut (x, 0) = 4 sin(x/3) − 6 sin(x)
9. Find the solution of the following PDE:
utt − uxx = 0
u(0, t) = u(1, t) = 0
u(x, 0) = 0
ut(x, 0) = x(1 − x)
10. Find the solution of the following PDE:
(1/2t+1)ut − uxx = 0
u(0,t) = u(π,t) =...

Find a solution u(x, t) of the following problem utt = 2uxx, 0 ≤
x ≤ 2 u(0, t) = u(2, t) = 0 u(x, 0) = 0, ut(x, 0) = sin πx − 2 sin
3πx.

Use the eigenfunction expansion to solve utt = uxx + e −t
sin(3x), 0 < x < π u(x, 0) = sin(x), ut(x, 0) = 0 u(0, t) =
1, u(π, t) = 0.
Your solution should be in the form of Fourier series. Write
down the formulas that determine the coefficients in the Fourier
series but do not evaluate the integrals

(PDE)
WRITE down the solutions to the ff initial boundary problem for
wave equation in the form of Fourier series :
1. Utt = Uxx ; u( t,0) = u(t,phi) = 0 ; u(0,x)=1 , Ut( (0,x) =
0
2. Utt = 4Uxx ; u( t,0) = u(t,1) = 0 ; u(0,x)=x , Ut( (0,x) =
-x

Solve the below boundary value equation
1. Ut=2uxx o<x<pi 0<t
2. u(0,t) = ux(pi,t) 0<t
3. u(x,0) = 1-2x 0<x<pi

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