Help differential equations anyone?

In summary, the conversation is about solving a differential equation with initial value and its application in exponential/logistic growth. The solution to the equation is x = 11000e^(0.1t) - 10,000, which can be obtained by separating the variables and integrating. The person seeking help had not read the book and was unsure about how to solve the equation. They were advised to separate variables and integrate, which they later realized and thanked for the help.
  • #1
rainyrabbit
10
0

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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  • #2
Separate the variables.
 
  • #3
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.
 
  • #4
hah stupid of me thx. for your help.
 

FAQ: Help differential equations anyone?

What are differential equations?

Differential equations are mathematical equations that describe the relationship between a function and its derivatives. They are used to model a wide range of physical phenomena, including motion, growth, and decay.

Why are differential equations important?

Differential equations are important because they provide a powerful tool for understanding and predicting the behavior of complex systems in science and engineering. They are used to solve problems in fields such as physics, biology, economics, and engineering.

What are some common methods for solving differential equations?

Some common methods for solving differential equations include separation of variables, exact equations, and numerical methods such as Euler's method and the Runge-Kutta method. Other techniques, such as Laplace transforms and power series solutions, are also frequently used.

How can I improve my skills in solving differential equations?

To improve your skills in solving differential equations, it is important to first have a strong foundation in calculus, linear algebra, and ordinary differential equations. Practicing and solving a variety of problems, as well as studying different solution techniques, can also help improve your skills.

Can differential equations be applied to real-world problems?

Yes, differential equations can be applied to real-world problems in a variety of fields, including physics, biology, chemistry, economics, and engineering. They are used to model and predict the behavior of systems in the natural world, making them an essential tool for scientists and engineers.

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