Putnam 1939 A5

Take either (i) or (ii). (i) Solve the system of differential equations $\begin{array}{l} \frac{d x}{d t}=x+y-3 \\ \frac{d y}{d t}=-2 x+3 y+1 \end{array}$ subject to the conditions $x=y=0$ for $t=0$ . (page 101) (ii) A heavy particle is attached to the end $A$ of a light $\operatorname{rod} A B$ of length $a$ . The rod is hinged at $B$ so that it can turn freely in a vertical plane. The rod is balanced in the vertical position above the hinge and then slightly disturbed. Prove that the time taken to pass from the horizontal position to the lowest position is $\sqrt{\frac{a}{g}} \log _{e}(1+\sqrt{2})$

Dataset text PutnamGAP. Quoted with source.

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