# Re-post Solution to DE

1. Nov 6, 2014

### MACH2

1. The problem statement, all variables and given/known data
Solve DE: y' -2 y / (x + a) = -1 where a = constant

2. Relevant equations
y' + p(x) y = q(x) solving this DE with integrating factor.

3. The attempt at a solution
Use integrating factor (x+a) ^ -2 for above DE,

[ y'(x+a) ^ -2 ]' = - (x+a)^ -2 solving this DE we get

y = C(x+a)^2 + (x+a) this seems to be a solution, C = arbitrary constant

Is this the only solution??

2. Nov 6, 2014

### slider142

Yes, your 1-parameter family of solutions contains every particular solution. In fact, every equation of this form, when solved by multiplying by the integrating factor of the exponential of the integral of p, will yield a 1-parameter family of solutions that contains every particular solution, as long as p and q are continuous on the interval of the solution.

3. Nov 6, 2014

### Staff: Mentor

The above isn't right. The left side is [y * (x + a)-2]', or in another form d/dx[y * (x + a)-2].

4. Nov 6, 2014

### MACH2

(x+a)^-2 = (x+a) elevated to the -2 power (I am not used to this sites equation editor)

5. Nov 6, 2014