# First Order Non-Linear Differential Equation (1 Viewer)

### Users Who Are Viewing This Thread (Users: 0, Guests: 1)

#### Nathan W0

1. The problem statement, all variables and given/known data
(x+y)dx-(x-y)dy=0

2. Relevant equations

3. The attempt at a solution
The solution is c=arctan^-1(y/x)-(1/2)*ln(x^2+y^2) but I don't know how to get the answer. If someone could explain how to solve the above DE, that would be great.

#### hunt_mat

Homework Helper
The DE is of te form:
$$\frac{dy}{dx}=\frac{x+y}{x-y}$$
Use the following substitution $$y(x)=xv(x)$$ The equation will become solvable.

Mat

#### Nathan W0

Oh, Okay I understand it now. Is there any way to know what substitution you would need to use?

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving