This is from a Diff EQ but but its just algebra i think?

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SUMMARY

The discussion centers on solving the differential equation (y/k) = (ynot/k) / ((ynot/k) - [1(ynot/k)]e^(-rt)) for t. The solution provided simplifies to e^(-rt) = {(ynot/k)(1-(y/k))}/{(y/k)(1-(ynot/k))}. The user expresses frustration in understanding the algebraic steps involved and seeks clarification on the notation, specifically whether ynot represents dy/dt. Additionally, they request recommendations for software that can assist in visualizing algebraic solutions.

PREREQUISITES
  • Understanding of differential equations, specifically first-order linear equations.
  • Familiarity with algebraic manipulation and exponential functions.
  • Knowledge of mathematical notation, including variables like y, ynot, and constants such as k and r.
  • Experience with mathematical software tools for solving equations, such as Wolfram Alpha or MATLAB.
NEXT STEPS
  • Research how to manipulate exponential equations in differential equations.
  • Learn to use Wolfram Alpha for step-by-step algebraic solutions.
  • Explore MATLAB's symbolic toolbox for solving differential equations.
  • Study the implications of variable notation in differential equations, particularly the role of initial conditions.
USEFUL FOR

This discussion is beneficial for students studying differential equations, educators teaching algebraic manipulation, and anyone seeking to enhance their problem-solving skills in mathematics.

HappMatt
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this is from a Diff EQ but but its just algebra i think??

I'm just working through an example here and its say to solve the equation

(y/k)=(ynot/k)/((ynot/k)-[1(ynot/k]e^(-rt))

for t. then in the next line it shows it solved for

e^(-rt)={(ynot/k)(1-(y/k)}/{(y/k)(1-(ynot/k)}

now i have been trying to fihure this out for awhile and its frustrating me, and i just can't seem to move on until i understand what I am not doing. can someone show me the steps involved in solving for e^(-rt) before i thrash this book or also recommend a program that will show algebraic steps in solving equation so that i don't have to spend hours figuring my retarted math mistakes out.
 
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Is ynot dy/dt?

And why do you multiply ynot/k by 1 in the first equation you posted? It looks like it may be a typo
 

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