Zill DE text says (y-x)dx+(4xy)dy=0 can be rewritten as....

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It is possible that the original equation was meant to be (y-x)dx+(4xy)dy=ydx or (y-x)dx+(4xy)dy=xdy, which would result in the equations you got. It is always important to double check for typos and errors in equations, as they can drastically change the solution.
  • #1
deltapapazulu
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Zill DE text says (y-x)dx+(4xy)dy=0 can be rewritten as:

4xy'+y=x

Am I missing something? I got 4xyy'+y=x instead.

Very rarely have I ever required starting a thread in a forum to resolve something as seemingly trivial as this but I just want to verify whether this is a typo or not.

Here are the steps I took:

The original is: (y-x)dx+(4xy)dy = 0

From there I got:

(4xy)dy=(x-y)dx

then

(4xy)dy/dx = x-y

then

(4xy)y'+y=x or 4xyy'+y=x
 
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  • #2
Your reasoning looks correct. Perhaps the text has a typo.
 

Related to Zill DE text says (y-x)dx+(4xy)dy=0 can be rewritten as....

1. What is the meaning of the equation (y-x)dx+(4xy)dy=0?

The equation (y-x)dx+(4xy)dy=0 is a differential equation that relates the rate of change of two variables, x and y, to each other. It represents a relationship between the two variables that must be satisfied for the equation to hold true.

2. Can the equation (y-x)dx+(4xy)dy=0 be rewritten in a different form?

Yes, the equation (y-x)dx+(4xy)dy=0 can be rewritten in different forms, depending on the context and the purpose of the equation. For example, it can be rewritten in terms of one variable in order to solve for a specific solution or to graph the equation.

3. How can (y-x)dx+(4xy)dy=0 be solved?

(y-x)dx+(4xy)dy=0 is a first-order linear differential equation, which means it can be solved using the methods of separation of variables, integrating factors, or using a substitution. The exact method used will depend on the specific form of the equation and the variables involved.

4. What are some real-life applications of (y-x)dx+(4xy)dy=0?

The equation (y-x)dx+(4xy)dy=0 has many real-life applications in fields such as physics, engineering, and economics. For example, it can be used to model the growth of populations, the spread of diseases, or the flow of fluids in pipes.

5. Why is it important to understand (y-x)dx+(4xy)dy=0 as a scientist?

As a scientist, understanding equations such as (y-x)dx+(4xy)dy=0 is crucial for solving complex problems and predicting outcomes. This type of equation is commonly used in various scientific fields, and being able to manipulate and interpret it is essential for conducting research and making accurate predictions.

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