Homework Help: 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