Differential Equation question

lilshai

New member
Joined
Sep 25, 2005
Messages
36
Hello...

I have this first order differential equation that says
e^((-5x))*y' - 5e^((-5x))*y = 0 and then it simplifies to:

d/dx(ye^(-5x)) = 0

How in the world did they (the book) get this??

Thank you.
 
Maybe they noticed the pattern in the two terms. Try differentiating f(x) = e<sup>-5x</sup>. What do you get?

So if you have ye<sup>-5x</sup> = 0, what will you get if you differentiate implicitly with respect to x?

Eliz.

P.S. I'm not saying that this is "the" way to do it, but, until somebody comes along with a proper methodology, this at least gives you a hint of a possibly-useful way to look at things.
 
Stare at the "Product Rule" really hard. It will soak in.
 
Hello,
I noticed that if I differentiate ye^((-5x)=0 I get exactly the step before it, e^((-5x))*y' - 5e^((-5x))*y = 0 using the product rule and implicit differentiation, so that makes sense. but how would you know how to go the other way around? Is there a method or do you just look for patterns?
 
Learning to recognize patterns is a lifelong process. Pursue it with vigor.

You do NOT want to miss an exact differential when it is staring at you.
 
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