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Using the Laplace transform to solve the partial differential equation utt=a²uxx , x>0, t>0 with boundary conditions u(0,t) = t² , limx→∞ u(x,t)=0 u(x,0)=0 , ut(x,0)=0 we obtain that the solution is given by u(x,t)=(t−1/a)² u1/a(t)) True or false?

Using the Laplace transform to solve the partial differential equation utt=a²uxx , x>0, t>0 with boundary conditions u(0,t) = t² , limx→∞ u(x,t)=0 u(x,0)=0 , ut(x,0)=0 we obtain that the solution is given by u(x,t)=(t−1/a)² u1/a(t)) True or false?

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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Using the Laplace transform to solve the partial differential equation

utt=a²uxx , x>0, t>0

with boundary conditions

u(0,t) = t² , limx→∞ u(x,t)=0

u(x,0)=0 , ut(x,0)=0 we obtain that the solution is given by u(x,t)=(t−1/a)² u1/a(t))

 

True or false?

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