Question

Find the differential equation representing the curve y = cx + c².

Answer 1

The equation of the given curve is
y = cx + c²            .....(1)
Differentiating both side of (1) with respect to x, we get

`dy/dx=c  `

Substituting `c=dy/dx` in (1), we get

`y=x dy/dx+(dy/dx)^2`

`=>(dy/dx)^2+x dy/dx−y=0`

This is the differential equation, which is representing the given curve.