Question

Use the method of separation of variables to solve the 1-dimensional wave equation uxx = 1/16utt over x ? (0,4), t ? (0,?), for the boundary conditions u(0,t) = u(4,t) = 0 and initial conditions u(x,0) = 12 sin(2?x) - 6 sin(8?x) and ut(x,0) = 0. Choose K as negative, say K = -?^2 (for the separation constant).

          Use the method of separation of variables to solve the 1-dimensional wave equation

uxx = 1/16utt over x ? (0,4), t ? (0,?), for the boundary conditions

u(0,t) = u(4,t) = 0 and initial conditions u(x,0) = 12 sin(2?x) - 6 sin(8?x) and
ut(x,0) = 0. Choose K as negative, say K = -?^2 (for the separation constant).

Use the method of separation of variables to solve the 1-dimensional wave equation

uxx = 1/16utt over x ? (0,4), t ? (0,?), for the boundary conditions

u(0,t) = u(4,t) = 0 and initial conditions u(x,0) = 12 sin(2?x) - 6 sin(8?x) and
ut(x,0) = 0. Choose K as negative, say K = -?^2 (for the separation constant).

Added by Seth M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sutara K

Step 1

First, we separate the variables by assuming that the solution can be written as a product of two functions, one depending on x and the other depending on t: u(x, t) = X(x)T(t). Show more…

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Use the method of separation of variables to solve the 1-dimensional wave equation uxx = 1/16utt over x ∈ (0,4), t ∈ (0,∞), for the boundary conditions u(0,t) = u(4,t) = 0 and initial conditions u(x,0) = 12 sin(2πx) - 6 sin(8πx) and ut(x,0) = 0. Choose K as negative, say K = -λ^2 (for the separation constant).