Paper 2, Section I, B

The following equation arises in the theory of elastic beams:

$t^{4} \frac{d^{2} u}{d t^{2}}+\lambda^{2} u=0, \quad \lambda>0, t>0$

where $u(t)$ is a real valued function.

By using the change of variables

$t=\frac{1}{\tau}, \quad u(t)=\frac{v(\tau)}{\tau},$

find the general solution of the above equation.

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