A5

Part of 1975 Putnam

Problems(1)

Source: Putnam 1975

I\subset \mathbb{R}

be an interval and

f(x)

a continuous real-valued function on

I

y_1

y_2

be linearly independent solutions of

y''=f(x)y

taking positive values on

I

. Show that for some positive number

k

k\cdot\sqrt{y_1 y_2}

is a solution of

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

Putnamfunctiondifferential equation