The general solution of the differential equation dy − 0.2x dx = 0 is a family of curves. These curves are all

Question

The general solution of the differential equation dy − 0.2x dx = 0 is a family of curves. These curves are all

 lines 

hyperbolas 

parabolas 

ellipses

Answer 1

If we manipulate the given equation to get dy/dx on one side, the equation becomes dy/dx = .2x. If we then find the antiderivative of this, we get y = .1x² + C. Since this equation has only one squared variable in it, then it must belong to the family of curves known as parabolas.