(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known dataReduce the order of a Cauchy-Euler Equation

2. Relevant equations[itex] x = e^t \mbox{ and } \ln x = t [/itex]

3. The attempt at a solution

[itex] \displaystyle \frac{d y}{d x} = \displaystyle \frac{d y}{d t} \displaystyle \frac{d t}{d x} = \displaystyle \frac{d y}{d t} \cdot \displaystyle \frac{1}{x}

[/itex]

and thus

[itex]

\displaystyle \frac{d^2 y}{d x^2} = \displaystyle \frac{d y}{d t} \cdot \displaystyle \frac{-1}{x^2} + \displaystyle \frac{1}{x} \displaystyle \frac{d}{d x} \Bigl ( \displaystyle \frac{d y}{d t} \Bigl )

[/itex]

Here is where I am getting stuck, specifically on [itex] \displaystyle \frac{d}{d x} \Bigl ( \displaystyle \frac{d y}{d t} \Bigl )

[/itex] this step. I know what I should get...

[itex]

\displaystyle \frac{1}{x} \Bigl ( \displaystyle \frac{d^2 y}{d t^2} \cdot \displaystyle \frac{1}{x} \Bigl )

[/itex]

But uhhh not getting it. Thanks in advance!

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