Question

Differential equation that is a function of x only will produce a slope field with parallel tangents along the diagonal will produce a slope field that does not have rows or columns of parallel tangents will produce a slope field with rows of parallel tangents will produce a slope field with columns of parallel tangents

Answer 1

Will produce 'a slope with columns of parallel tangents'.

Explanation:

We have that the differential equation is a function of x only.

i.e.
`(dy)/(dx)=f(x)`.

Let, F(x) be the anti-derivative if f(x) i.e.
`F(x)=\int f(x)`

So, the differential equation gives,

`(dy)/(dx)=f(x)`.

`y=\int f(x)+c`

i.e. y = F(x) + c.

That means the general solution of the differential equation is a family of curves which are vertical copies of any one of them.

Hence, the differential equation that is a function of x only will produce 'a slope with columns of parallel tangents'.