# Differential equation dy/dx = 2y-4x

1. Mar 30, 2009

### nns91

1. The problem statement, all variables and given/known data

Consider the differential equation dy/dx = 2y-4x

a. Find the value of b for which y=2x+b is a solution to the given differential equation

b.Let g be the function that satisfies the given differential equation with the initial condition g(0)=0. Does the graph of g have a local extremum at the point (0,0) ? If so, is the point a local maximum or minimum

2. Relevant equations

integration, derivative

3. The attempt at a solution

a. So I choose point (1,0) and plug in y=2x+b and solve for b=1. Then I have y=2x+1. AM I right ? It seems too easy to be right. Is it harder than I thought ?

b. So do I have to integrate ? I found that (0,0) is a critical point. How do I move on ?

2. Mar 30, 2009

### rock.freak667

For part a) what you need to do is find dy/dx from your given solution and then substitute y in the differential equation and find b. Can you do that?

It would be beneficial to solve the differential equation.

3. Mar 30, 2009

### nns91

a. Got cha.

b. is g(x)= 2x+1 ? Am I right ? It sounds wrong

4. Mar 30, 2009

### rock.freak667

Do you know how to solve 1st order DEs of the form
$$\frac{dy}{dx}+P(x) y=Q(x)$$

via an integrating factor?

5. Mar 30, 2009

### nns91

Yeah. so is the integrating factor only e^2 ?
I got the final equation as y=-2x^2. Am I right ?

6. Mar 30, 2009