# Help Solving a Diff. Equation: Ideas Needed

• manenbu
In summary, the conversation revolves around solving a differential equation with the given equation and attempts at finding a solution. The suggested method of substitution using v = y/x and v = x/y is discussed, leading to a successful solution.
manenbu
Need help with solving this DE.

## Homework Statement

$$(x e^{\frac{y}{x}} + 2x^2 y)dy - y e^{\frac{y}{x}}dx = 0$$

## The Attempt at a Solution

Well, I don't even know where to start. It's not exact, and I can't make it exact with an integrating factor. All of this y/x in here makes me think that maybe I need to make a substitution here, but I can't just use it like that because it wouldn't work.
Any ideas?

I would start with v = y/x. I can't guarantee that it would work, since I haven't worked the problem, but it might be what you need to get an exact equation.

The substitution v = y/x is equivalent to y = vx, so y' = v + v'x.

Try using the substitution v = x/y which is equivalent to vy = x

So dx/dy = v + y*dv/dy

Give it a try and see if it works.

Yes it was, but I also had to make a substitution for y, missed it the first time.
Got it right now.

Thanks.

## 1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is used to model physical phenomena and is an important tool in many fields of science and engineering.

## 2. Why is solving a differential equation important?

Solving a differential equation allows us to understand and predict the behavior of complex systems and phenomena. It is used in a wide range of scientific fields, including physics, chemistry, biology, and engineering.

## 3. What are some techniques for solving differential equations?

There are several techniques for solving differential equations, including separation of variables, substitution, and using special functions such as Laplace transforms and power series. The most appropriate technique depends on the specific equation and the problem being solved.

## 4. How can I check if my solution to a differential equation is correct?

You can check your solution by plugging it back into the original equation and verifying that it satisfies the equation. You can also use numerical methods, such as graphing, to compare your solution to the behavior of the system in question.

## 5. Are there any resources available to help me solve a differential equation?

Yes, there are many resources available, both online and in textbooks, to help you solve differential equations. You can also consult with a math or science tutor for personalized assistance.

Replies
7
Views
1K
Replies
3
Views
844
Replies
4
Views
521
Replies
3
Views
243
Replies
5
Views
1K
Replies
8
Views
1K
Replies
18
Views
2K
Replies
19
Views
2K
Replies
4
Views
1K
Replies
20
Views
979