Separable Differential Equations

In summary, the task is to separate the differential equation by bringing the n and dn to one side and the dt to the other side. Then, integrate both sides of the equation.
  • #1
olicoh
24
0

Homework Statement


Suppse dn/dt = 1/10n and n(1)=-2. Separate the differential equation, then integrate both sides.

The Attempt at a Solution


How do I do this? There is no 't' to 'separate' from the equation. Would it just be:
int[1/10n] = int[0t] ?
 
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  • #2
Hi olicoh! :smile:

You'll need to bring the n and the dn to one side, and the dt to the other side first. Then you'll need to integrate...
 
  • #3
micromass said:
Hi olicoh! :smile:

You'll need to bring the n and the dn to one side, and the dt to the other side first. Then you'll need to integrate...

So would it be: int[10]dt = int[n]dn?
 
  • #4
No. That 10 should be 1/10...
 
  • #5
Is the equation dn/dt= 1/(10n) or dn/dt= (1/10)n ?
 

What are separable differential equations?

Separable differential equations are a type of differential equation where the variables can be separated into two functions that are then integrated separately.

What is the process for solving separable differential equations?

The process for solving separable differential equations involves separating the variables, integrating each side separately, and then solving for the constant using initial conditions.

What is the purpose of solving separable differential equations?

Solving separable differential equations allows us to model and understand many real-world phenomena, such as population growth and decay, chemical reactions, and radioactive decay.

What are the common techniques used to solve separable differential equations?

The most common techniques used to solve separable differential equations include separation of variables, substitution, and integration by parts.

What are some applications of separable differential equations in science?

Separable differential equations are commonly used in physics, chemistry, and biology to model and predict various natural processes, such as the motion of objects, chemical reactions, and population growth.

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