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The solution of the wave equation Urx Gutt. 0 < r < 3. t > 0, which satisfies the boundary conditions u(0, t) = u(3, t) = 0 and the initial conditions u(x, 0) uz(r, 0) = 2 sin () - 3 sin(2r2) + 2 sin(37z) is 0 and -- u(x, t) = E E sin () [an cos (2t) + b, sin (2t)] 2nnt COS where n=1 O a) b1 = 2, b6 -3, bg = 2, bn O otherwise an O b) b1 = , , be = 7, b9 =+, b, = an = 0 otherwise Od ai an = bn O otherwise a6 4元) ag 2, a6 -3, ag =2, an O otherwise d) ai O e) None of these

The solution of the wave equation Urx Gutt. 0 < r < 3. t > 0, which satisfies the boundary conditions u(0, t) = u(3, t) = 0 and the initial conditions u(x, 0) uz(r, 0) = 2 sin () - 3 sin(2r2) + 2 sin(37z) is 0 and -- u(x, t) = E E sin () [an cos (2t) + b, sin (2t)] 2nnt COS where n=1 O a) b1 = 2, b6 -3, bg = 2, bn O otherwise an O b) b1 = , , be = 7, b9 =+, b, = an = 0 otherwise Od ai an = bn O otherwise a6 4元) ag 2, a6 -3, ag =2, an O otherwise d) ai O e) None of these

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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The solution of the wave equation Urx Gutt. 0 < x < 3. t > 0, which satisfies the boundary conditions u(0, t) = u(3, t) = 0 and the initial conditions u(x, 0) Ut(x, 0) = 2 sin() - 3 sin(2rx) + 2 sin(3rz) is O and -- 2nnt. u(x, t) = E sin () [an cos (2at) + b, sin COS 3 where 3 n=1 O a) b1 = 2, b6 -3, bg = 2, bn O otherwise an O b) b1 = , , be = 7, bg ==, b, = an = 0 otherwise C a1 an = bn O otherwise a6 47 ag -3, ag 2, an 0 otherwise d) ai 2, a6 O e) None of these
Transcribed Image Text:The solution of the wave equation Urx Gutt. 0 < x < 3. t > 0, which satisfies the boundary conditions u(0, t) = u(3, t) = 0 and the initial conditions u(x, 0) Ut(x, 0) = 2 sin() - 3 sin(2rx) + 2 sin(3rz) is O and -- 2nnt. u(x, t) = E sin () [an cos (2at) + b, sin COS 3 where 3 n=1 O a) b1 = 2, b6 -3, bg = 2, bn O otherwise an O b) b1 = , , be = 7, bg ==, b, = an = 0 otherwise C a1 an = bn O otherwise a6 47 ag -3, ag 2, an 0 otherwise d) ai 2, a6 O e) None of these
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