, where x does not equal zero
I was to find the particular solution of this equation with the initial condition f(-1) = 1. I did so and found y = -1 (hopefully this is correct!)
However, I'm also asked to give the domain of this solution. I'm really confused about when you should and shouldn't restrict domain (when to have absolute value signs on ln, for example), so I don't know how to answer this.
Help, please?
The DE can be written as...
(1)
... so that it is linear. In similar situation it is requested that the coefficient of the term doesn't vanish so that it must be and that determines the domain of the solutions. The DE can be resolved with the 'standard' method of sepation of variables and we obtain...
(2)
With the 'initial condition' the soltution is ...
Kind regards
The fact is that the general solution is...
(1)
... being c an 'arbitrary constant'. That means symply that You are not able to impose any 'initial conditions' in different from , but also in this case You able to derive the value of because all solutions 'pass' from the point ...
Kind regards