Question

Differential equation corresponding to the family of curves y= c(x-c)^2, where c iz an arbitrary constant

Answer 1

Answer:

y(y')^3 = x^2y'(y'-1)+2y(x-2y) is the required equation

Step-by-step explanation:

find the differential equation of the family of curves y=c(x-c)^2 c is parameter

y=c(x-c)^2 c is parameter

Homework help Donate

A)

y = c(x-c)^2-------(1)

y' = 2c(x-c)-------(2)

dividing both hte equations

y/y' = x-c/2

2y/y' = (x-c)

c = x-2y/y'

substituting this in equ (1) and simplifying we get,

y(y')^3 = x^2y'(y'-1)+2y(x-2y) is the required equation