Help differential equations anyone?

[rainyrabbit]

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. ^^

 

[neutrino]

Separate the variables.

 

[HallsofIvy]

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 $$\frac{dx}{dt}= 1000- 0.10x$$ you can easily get
$$\frac{dx}{1000- 0.10x}= dt$$ and integrate.

 

[rainyrabbit]

hah stupid of me thx. for your help.