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

Expert Solution

Colby Messinger answered 1 year ago

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

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 this Initial Value Problem using the Laplace transform: x''(t) - x'(t) - 6x(t) = e^(4t),...

Solve this Initial Value Problem using the Laplace transform: x''(t) - x'(t) - 6x(t) = e^(4t), x(0) = 1, x'(0) = 1

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)

Use Laplace transformations to solve the following ODE for x(t): x¨(t) + 2x(t) = u˙(t) +...

Use Laplace transformations to solve the following ODE for x(t): x¨(t) + 2x(t) = u˙(t) + 3u(t) u(t) = e^−t Initial conditions x(0) = 1, x˙(0) = 0, u(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 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

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

1) Find f(x) by solving the initial value problem. f' (x) = e x − 2x;...

1) Find f(x) by solving the initial value problem. f' (x) = e x − 2x; f (0) = 2 2) A rectangular box is to have a square base and a volume of 20f t^3 . If the material for the base costs 30¢/f t^2 , the material for the sides costs 10¢/ft^2 , and the material for the top costs 20¢/f t^2 , determine the dimensions of the box that can be constructed at minimum cost.

Use Laplace transforms to solve the initial value problem: x' = 2x + y, y' =...

Use Laplace transforms to solve the initial value problem: x' = 2x + y, y' = 6x + 3y; x(0) = 1, y(0) = -2

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