The differential equation for transverse vibrations of a string whose density increases linearly from one end to the other is y + (Ax + B)y = 0, where A and B are constants. Find the general solution of this equation in terms of Bessel functions. Hint: Make the change of variable Ax + B = Au.
The differential equation for transverse vibrations of a string whose density increases linearly from one end to the other is y + (Ax + B)y = 0, where A and B are constants. Find the general solution of this equation in terms of Bessel functions. Hint: Make the change of variable Ax + B = Au.
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The differential equation for transverse vibrations of a string whose density increases linearly from one end to the other is y + (Ax + B)y = 0, where A and B are constants. Find the general solution of this equation in terms of Bessel functions. Hint: Make the change of variable Ax + B = Au.
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