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.