Consider the Cauchy problem for the linear one-dimensional wave equation 9 Uzz for x €R and t > 0, = "n u(r,0) = f(x) for r E R, u(r, 0) = g(x) for r E R, where f e C²(R) and g E C'(R). Show that if ƒ is an odd function and g is an even function, then for every fixed t > 0, we have uz(0,t) = f'(3t).

Consider the Cauchy problem for the linear one-dimensional wave equation 9 Uzz for x €R and t > 0, = "n u(r,0) = f(x) for r E R, u(r, 0) = g(x) for r E R, where f e C²(R) and g E C'(R). Show that if ƒ is an odd function and g is an even function, then for every fixed t > 0, we have uz(0,t) = f'(3t).

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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