Quick question about differential equations

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Homework Help Overview

The discussion revolves around solving a differential equation of the form dy/dx = y/x. Participants are exploring the manipulation of logarithmic expressions and constants in the context of this equation.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to derive the solution by separating variables and integrating, questioning the transition from logarithmic forms to the final expression. Other participants suggest examining the properties of exponents and constants in relation to the solution.

Discussion Status

Participants are engaging in a back-and-forth exploration of the manipulation of logarithmic and exponential forms. Some guidance has been offered regarding the treatment of constants, but there is no explicit consensus on the steps leading to the final solution.

Contextual Notes

There is an implicit assumption that the participants are familiar with the properties of logarithms and exponentials, as well as the rules for solving differential equations. The original poster expresses uncertainty about the simplification process.

vande060
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Homework Statement



solve the equation

dy/dx = y/x



Homework Equations





The Attempt at a Solution



dy/dx = y/x

dy/y = dx/x

lny = lnx + c

my book gives the answer

y = kx

not sure how they got that, did they just take the log of the constant, because its just a constant and can be manipulated to simplify.

y = lnx + lnc

y = ln(xc)

k = c

y = kx ??
 
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Look at:

e^{\ln(y)}=e^{\ln(x)+C}
 
SammyS said:
Look at:

e^{\ln(y)}=e^{\ln(x)+C}

would that be the same as saying

y = xec
 
Yes. And ec is just a constant, which you can call k.
 
Mark44 said:
Yes. And ec is just a constant, which you can call k.

well that was easy thanks
 

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