# Differential equation of dy/dx = (2x-y+4)/ (4x-2y +1)

1. Feb 17, 2016

### hotjohn

1. The problem statement, all variables and given/known data
I'm asked to use the transformation of v= 2x-y to solve dy/dx = (2x-y+4)/ (4x-2y +1)

the answer given is (2/9)(6x-3y-2) +(7/9)ln(6x-3y-2) = x +c , i got (2/9)(6x-3y) +(7/9)ln(6x-3y-2) = x +c , what's wrong with my working ?

2. Relevant equations

3. The attempt at a solution

#### Attached Files:

• ###### 256.jpg
File size:
29.4 KB
Views:
54
2. Feb 17, 2016

### Staff: Mentor

The two answers differ by a constant summand of 4/9. As you have "+c" anyway, this difference does not matter.

3. Feb 18, 2016

### hotjohn

lol , why the author wanna dd in another (2/9)(-2) into the answer ? this is confusing ...

4. Feb 18, 2016

### HallsofIvy

Staff Emeritus
Presumably, because the author used a different method to arrive at a solution. In any case, the point is that, because the derivative of a constant is 0, two functions, differing by a constant, can be solutions to the same first order differential equation.