Differential equation involving a time series

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SUMMARY

The discussion focuses on solving a differential equation involving a time series, specifically the function f(n,t) defined as f(n,t)=f(n,0)e^{kt} + e^{kt} - dn^2. The user seeks guidance on techniques for solving this equation and understanding its implicit nature. Key aspects include the importance of initial conditions in determining the solution. The equation suggests an exponential growth model influenced by time and quantity.

PREREQUISITES
  • Understanding of differential equations (DEs)
  • Familiarity with exponential functions and their properties
  • Knowledge of initial value problems in calculus
  • Basic concepts of time series analysis
NEXT STEPS
  • Research techniques for solving implicit differential equations
  • Learn about initial value problems and their applications in modeling
  • Explore time series forecasting methods
  • Study the implications of exponential growth in mathematical modeling
USEFUL FOR

Mathematicians, data scientists, and anyone involved in modeling time-dependent phenomena using differential equations.

AbusesDimensAnalysis
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Hey all, it's been awhile since done any calculus or DE's but was trying out some modelling (best price price per item for bulk value deals as a function of time and amount), in the last line i have f(n,t) implicitly.

Any pointers or techniques for solving such things?

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Why is it implicitly? You have ##f(n,t)=f(n,0)e^{kt} + e^{kt} -dn^2## if I saw this correctly (it's a bit tiny for my old eyes). Looks as if you only have to figure out the initial conditions.
 

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