I obtained an extra factor of ##\frac{1}{l^2}## in the first term on the LHS of (3.34).(adsbygoogle = window.adsbygoogle || []).push({});

From (3.33),

LHS ##=u^2\frac{d}{d\theta}(\frac{u^2}{m}\frac{du}{d\theta}\frac{dr}{du})-\frac{l^2u^3}{m}##

##=u^2\frac{d}{d\theta}(-\frac{1}{m}\frac{du}{d\theta})-\frac{l^2u^3}{m}##

##=-\frac{u^2}{m}\frac{d^2u}{d\theta^2}-\frac{l^2u^3}{m}##

Multiplying throughout by ##-\frac{m}{l^2u^2}##, we have

LHS ##=\frac{1}{l^2}\frac{d^2u}{d\theta^2}+u##

which differs from (3.34).

What's wrong?

EDIT: I found the mistake. The text has a typo. The "1"s in (3.33) are actually "##l##"s.

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# B Recast a differential equation with a change of variable

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