Separable Differential Equation

In summary, the conversation is about a high school homework assignment involving solving for v. The question is whether or not the -64/5 in the last two lines of the provided image is necessary. The response is that it is necessary in order for the original differential equation to be satisfied. The conversation ends with the speaker expressing their appreciation for the helpful forums and their belief that they are learning more from them than from their expensive education.
  • #1
mlowery
23
0
Hello,
Yes, this is for a class - but it is simply a high school homework assignment.
I am solving for v. (This is only part of the homework problem, BTW).
http://mlowery.t35.com/AP_4_1a.jpg
My question is particularly concerned with the last two lines. On the final line, is the [tex]-64/5[/tex] necessary?

Thanks,
Mitchell
 
Last edited by a moderator:
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  • #2
of course. you can verify that otherwise, the original differential equation is not satisfied.
 
  • #3
Thanks man. I guess I just wasn't thinking.

BTW, I am very impressed by these forums. It is a great resource and there are many interesting things to read.

Thanks,
Mitchell
 
  • #4
It's great. There are so many knowledgeable people around. I sometimes feel like I'm learning more here than I do at school for 3000$ a year. :grumpy:
 
  • #5
Haha, I guess I will find out next year.
 

1. What is a separable differential equation?

A separable differential equation is a type of differential equation that can be written in the form of dy/dx = f(x)g(y), where f(x) and g(y) are functions of x and y, respectively. This type of equation can be solved by separating the variables and integrating both sides.

2. Why are separable differential equations important?

Separable differential equations are important because they have a wide range of applications in various fields of science, including physics, engineering, biology, and economics. They can be used to model and solve many real-world problems involving rates of change.

3. How do you solve a separable differential equation?

To solve a separable differential equation, you first need to separate the variables on both sides of the equation. Then, you can integrate both sides and add a constant of integration. Finally, you can solve for the dependent variable to get the general solution.

4. Can all differential equations be solved by separation of variables?

No, not all differential equations can be solved by separation of variables. Only certain types of equations, such as separable, homogeneous, and exact differential equations, can be solved using this method. Other types, such as non-linear and non-separable equations, require different techniques for solving.

5. What are some common applications of separable differential equations?

Some common applications of separable differential equations include population growth and decay, radioactive decay, Newton's law of cooling, and drug concentration in the body. They can also be used to model the motion of objects under the influence of gravity and air resistance, as well as electric circuits and chemical reactions.

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