In Problems 1-20 solve the given boundary-value problem by an appropriate integral transform. Make assumptions about boundedness where necessary.
1.
u(x, 0) = 0,
The solution of the given boundary value problem under given boundary conditions.
Answer to Problem 1RE
The solution of boundary value problem is
Explanation of Solution
Given:
The given boundary value problem is
Calculation:
The given boundary value problem is,
Take Fourier transform on both sides of the above equation,
Therefore, the equation is,
Apply Fourier cosine transform then the particular solution of the above equation is,
At the given boundary condition
Substitute the value of
At boundary condition,
Take Fourier transform of the above equation,
Partially differentiate the equation (3) with respect to
Equate the equations (4) and (5),
Substitute the value of
Take inverse Fourier transform of the above equation and apply Fourier cosine transform,
Thus, the solution of boundary value problem is
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Chapter 14 Solutions
Differential Equations with Boundary-Value Problems
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