Solving for du/dt: tdt= \frac{2+2u-du}{1+u}

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In summary, the conversation discussed how to manipulate the equation \frac{du}{dt}=2+2u+t+tu to make it easier to solve. The equation was factored to show that it can be separated into two simpler equations.
  • #1
suspenc3
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[tex] \frac{du}{dt}=2+2u+t+tu[/tex]

I manipulated it to:[tex]-tdt= \frac{2+2u-du}{1+u}[/tex]

Should it be in this form? or try something else?
 
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  • #2
suspenc3 said:
[tex] \frac{du}{dt}=2+2u+t+tu[/tex]


Note that 2 + 2u + t + tu, can be factored.

First factor the 2 from the first two terms leaving
2(1+u) + t + tu
Then factor the t from the last two terms and you have
2(1+u) + t(1+u)
Now you should notice that you have a common term of (1+u) which can be factored out leaving
(2+t)(1+u)
And now you can easily separate this equation.
 
  • #3
Riight, I see it now, Thanks
 
  • #4
suspenc3 said:
Riight, I see it now, Thanks

No problem glad I could help.
 

1. What is the purpose of solving for du/dt?

Solving for du/dt allows us to find the instantaneous rate of change of a variable u with respect to time t. This is important in many scientific fields, including physics, chemistry, and biology, as it helps us understand the behavior of systems over time.

2. How do you solve for du/dt?

To solve for du/dt, we first need to rearrange the given equation to isolate du/dt on one side. This may involve some algebraic manipulation, such as factoring or distributing. Once du/dt is isolated, we can then use differentiation techniques, such as the chain rule or product rule, to find its value.

3. What is the significance of the variable t in the equation?

The variable t represents time in the given equation. This means that the rate of change of u is being measured over time. This can help us understand how u is changing and evolving over a certain period of time.

4. Can this equation be solved for different variables besides u and t?

Yes, this equation can be solved for any two variables that are related by an equation. However, the process for solving for du/dt may vary depending on the specific variables and equation given.

5. What are some real-world applications of solving for du/dt?

Solving for du/dt has many real-world applications, such as determining the rate of change of population growth, predicting the spread of diseases, and analyzing the velocity of objects in motion. It is also commonly used in economic and financial models to understand the changing rates of various variables over time.

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