DIFFERENTIAL EQUATION ei guys need some help about this...?

Question

give the d.e. of the following:
1.)Straight line through origin.

2.)straight line with slope and y-intercept equal

3.)straight line with some algebraic sum of intercept fixed as k.

Answer 1

None of those require differential equations. Each is a simple descriptive problem of analytic geometry in the cartesian plane.

1. f(x)=mx
2. f(x)= mx+m =m (x+1)
3. f(x)= mx +k

If you want to get "differential" with these, note that m=df(x)/dx and substitute.

1. f(x)=x * df(x)/dx
2. f(x)=(x+1) * df(x)/dx
3. f(x)=x * df(x)/dx + k

Answer 2

The differential equation governing ANY straight line is: dy/dx = m
m = slope
As the previous poster noted, a line does not need a differential equation to describe it. Moreover, since any differential equation without associated boundary or initial conditions describes a family of curves, a differential equation alone is not sufficient to describe a given line.