Question

Find the differential equation of all non horizontal lines in a plane

Answer 1

Let y=mx+c,m≠0y=mx+c,m≠0 be the equation of all non-horizontal lines in a plane.

As it has two arbitrary constants mm and cc,we need to differentiate it two times.

y=mx+cy=mx+c

dydx=mdydx=m

d2ydx2=0d2ydx2=0

But my book says answer is d2xdy2=0d2xdy2=0.

Book gives this solution.

Let ax+by+c=0,a≠0ax+by+c=0,a≠0 be the equation of all non-horizontal lines in a plane.

Differentiating both sides wrt yy,

adxdy+b=0adxdy+b=0

ad2xdy2=0ad2xdy2=0

As a≠0,d2xdy2=0a≠0,d2xdy2=0