(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the differential equation [itex]\frac{dy}{dx}[/itex] = 2x - y

On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated, and sketch the solution curve that passes through the point (0, 1).

2. Relevant equations

[itex]\frac{du}{dx}[/itex] = u where u = 2x - y

3. The attempt at a solution

[itex]\frac{dy}{dx}[/itex] = 2x - y

[itex]\frac{du}{dx}[/itex] = u where u = 2x - y

u' = 2 - [itex]\frac{dy}{dx}[/itex]

Then what do I do? I have no clue where to go from here.

Is this a homogeneous differential equation?

I know what to do in regards to the rest of the problem, I just don't know how to separate so I can integrate. Do I use the substitution method or integrating factors?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: AP Test Practice DE

**Physics Forums | Science Articles, Homework Help, Discussion**