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Putnam 1975 A5

Source: Putnam 1975

February 17, 2022

Putnamfunctiondifferential equation

Problem Statement

Let

I\subset \mathbb{R}

be an interval and

f(x)

a continuous real-valued function on

I

. Let

y_1

and

y_2

be linearly independent solutions of

y''=f(x)y

taking positive values on

I

. Show that for some positive number

k

the function

k\cdot\sqrt{y_1 y_2}

is a solution of

y''+\frac{1}{y^{3}}=f(x)y

.

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