Solve the nonhomogeneous heat equation: ut-kuxx=sinx, 0<x<pi, t>0 u(0,t)=u(pi,t)=0, t>0 u(x,0)=0, 0<x<pi

Solve the nonhomogeneous heat equation:

ut-kuxx=sinx, 0<x<pi, t>0

u(0,t)=u(pi,t)=0, t>0

u(x,0)=0, 0<x<pi

Expert Solution

Colby Messinger answered 1 year ago

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < pi,...

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < pi, t > 0, u(0,t) = 0 = u(pi,t), u(x,0) = sinx - sin3x

Please solve the following: ut=uxx, 0<x<1, t>0 u(0,t)=0, u(1,t)=A, t>0 u(x,0)=cosx, 0<x<1

Consider the equation utt = uxx x ∈ (0, pi) ux(0,t) = u(pi,t) = 0 Write...

Consider the equation utt = uxx x ∈ (0, pi) ux(0,t) = u(pi,t) = 0 Write the series expansion for a solution u(x,t)

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

Find the solution to the heat equation on 0 < x < l, with u(0, t)...

Find the solution to the heat equation on 0 < x < l, with u(0, t) = 0, ux(l, t) = 0, and u(x, 0) = phi(x). This is sometimes called a "mixed" boundary condition.

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1,...

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1, t > 0, u(0,t) = 0 = u(1,t), u(x,0) = x/2

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1,...

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1, t > 0, ux(0,t) = 0 = ux(1,t), u(x,0) = 1 - x2

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.

7. Find the solution of the following PDEs: ut−16uxx =0 u(0,t) = u(2π,t) = 0 u(x,...

7. Find the solution of the following PDEs: ut−16uxx =0 u(0,t) = u(2π,t) = 0 u(x, 0) = π/2 − |x − π/2|

Solve y"+y=u(t-pi/2)+3 delta(t-3 pi/2)-u(t-2 pi), by laplace transform methods with y(0)=y'(0)=0.

Question

Solve the nonhomogeneous heat equation: ut-kuxx=sinx, 0<x<pi, t>0 u(0,t)=u(pi,t)=0, t>0 u(x,0)=0, 0<x<pi

Solutions

Expert Solution

Related Solutions

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < pi,...

Please solve the following: ut=uxx, 0<x<1, t>0 u(0,t)=0, u(1,t)=A, t>0 u(x,0)=cosx, 0<x<1

Consider the equation utt = uxx x ∈ (0, pi) ux(0,t) = u(pi,t) = 0 Write...

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

Find the solution to the heat equation on 0 < x < l, with u(0, t)...

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1,...

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1,...

Solve the following initial value problems: a) ut+xux= -tu, x is in R, t>0; u(x,0) =f(x),...

7. Find the solution of the following PDEs: ut−16uxx =0 u(0,t) = u(2π,t) = 0 u(x,...

Solve y"+y=u(t-pi/2)+3 delta(t-3 pi/2)-u(t-2 pi), by laplace transform methods with y(0)=y'(0)=0.