Paper 2, Section I, B

Differential Equations | Part IA, 2014

The following equation arises in the theory of elastic beams:

t4d2udt2+λ2u=0,λ>0,t>0t^{4} \frac{d^{2} u}{d t^{2}}+\lambda^{2} u=0, \quad \lambda>0, t>0

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

By using the change of variables

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

find the general solution of the above equation.

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