Help differential equations anyone?

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Homework Help Overview

The discussion revolves around solving a differential equation related to exponential growth, specifically in the context of population dynamics. The original poster presents an initial value problem involving the equation dx/dt = 1000 + 0.10x with an initial condition x(0) = 1000.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster seeks clarification on how a specific answer to the differential equation is derived, expressing uncertainty about the solution process. Some participants suggest separating variables as a potential method to approach the problem, while others indicate that there are multiple ways to solve the equation, depending on the course level.

Discussion Status

The discussion is ongoing, with participants offering guidance on potential methods for solving the differential equation. There is an acknowledgment of different approaches, but no consensus has been reached on a specific method or solution yet.

Contextual Notes

Participants note the possibility of varying methods based on the course level, indicating that the original poster may be at an introductory stage in their studies.

rainyrabbit
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Homework Statement



Differential equation: dx/dt = 1000 + 0.10x
x(0) = 1000
Solve the initial value problem for x as a function of t

Section of Exponential/Logistic growth; applications (population growth) ---- Intro-level calculus


Homework Equations



Answer: x = 11000e^(0.1t) - 10,000

The Attempt at a Solution



Sorry could you help me how this answer (found at the end of the book) is gotten? Sorry but I do not know how to do it; please help. ^^
 
Last edited:
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Separate the variables.
 
Have you tried actually reading the book? I don't mean to be harsh but there are several different ways to solve this equation and I don't know which one you are to learn at this point in your course. If you are at the beginning of the course then probably the simplest thing to do is what neutrino suggested: separate variables.
From [tex]\frac{dx}{dt}= 1000- 0.10x[/tex] you can easily get
[tex]\frac{dx}{1000- 0.10x}= dt[/tex] and integrate.
 
hah stupid of me thx. for your help.
 

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