Question

Question #0c06b

Answer 1

See below.

Explanation:

Solve this differential equation:

`dy/dx-1=0`

`->dy/dx=1`

`->intdy=intdx`

Solving for the general solution gives:

`y=x+C`

Where `C` is the constant of integration. As `C` is yet undetermined and can take any (complex) value we call this the general solution. `C` might be `+2` or `-3` (though without further information there is no reason it can't be something like `1,4,pi,sqrt(10)` or `1+i`). These two values of `C` would give us:

`y=x+2` or `y=x-3`

In these cases `C` has been determined so these are particular solutions. In other words they are just specific cases of the general solution. The value of `C` can usually be worked out when given "initial" or "boundary" conditions.

Answer 2

Please see below.

Explanation:

For `y = x-3` we have `dy/dx = 1` so `dy/dx - 1 =0`

And also, for for `y = x+2` we have `dy/dx = 1` so `dy/dx - 1 =0`