Given the partial differential equation Ut + Uxx = 0, 0 < x < ?, t > 0. Use the method of separation of variables to solve the given equation with the following conditions. Ux(0, t) = 0, t > 0 Ux(?, t) = 0, t > 0 U(x, 0) = x(? - x), 0 < x < ?
Added by Cody C.
Close
Step 1
Step 1: Assume a solution of the form U(x, t) = X(x)T(t). Show more…
Show all steps
Your feedback will help us improve your experience
Melissa Munoz and 54 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Given the partial differential equation Ut + Uxx = 0, 0 < x < T, t > 0. Use the method of separation of variables to solve the given equation with the following conditions: Ux(0, t) = 0, t > 0; Ux(T, t) = 0, t > 0; U(x, 0) = x(n - x), 0 < x < T.
Sri K.
Given the partial differential equation Ut + Uxx = 0, 0 < x < π, t > 0. Use the method of separation of variables to solve the given equation with the following conditions Ux(0, t) = 0, t > 0, Ux(π, t) = 0, t > 0, U(x, 0) = x(π - x), 0 < x < π.
Consider the following boundary and initial conditions and solve the given partial differential equation using the separation of variables method: ∂^2u/∂t^2 = 4∂^2u/∂x^2 u(0,t) = 0, for t > 0 u(4,t) = 0, for t > 0 ∂u(x,0)/∂t = 0, for 0 ≤ x ≤ 4 u(x,0) = x/3, for 0 ≤ x ≤ 4
Madhur L.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Watch the video solution with this free unlock.
EMAIL
PASSWORD