Well, your answer "dy/dx= m" isn't correct because you have not eliminated the parameter m!
From the original equation, y= mx, m= y/x which gives dy/dx= y/x.
Sketch a few members of the straight lines through the origin. By eliminating parameters, derive a differential equation which describes this family.
(since there are infinite gradients)
but the correct answer was: . I am not sure why.
Thanks. If instead the question was: find the differential equation for the straight lines through the point (2,3), what would the procedure be?
I tried using:
y = mx + c
3 = 2m + c
but differentiating it obviously wouldnt work, since there are only constants