Differential equation question

Question

A differential equation that is a function of y 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

The best way to understand is with a sketch. If the derivative of the function is a function of the dependent variable y only, then for a particular value of y only, the arrows you would draw should all be pointing in the same direction for all values of x. So if you were to sketch the slope field you would have rows of arrows such that all arrows in a given row would be pointing in the same direction. You would therefore have rows of parallel tangents. 

 

Note I'm assuming that: 

 

y'= f(y)