Question

Find the differential equation of the following 

(i) y = cx + c – c³ 

(ii) y = c(x – c)² 

(iii) xy = c² 

(iv) x² + y² = a²

Answer 1

(i) y = cx + c – c ……. (1) 

Here c is a constant which has to be eliminated 

Differentiating w.r.t x, dy/dx = c …… (2) 

Using (2) in (1) we get, 

y = (dy/dx)x + dy/dx - (dy/dx)³ which is the required differential equation. 

(ii) y = c(x – c) …… (1) 

We have to eliminate c 

Differentiating w.r.t x ,we get, dy/dx = 2c(x – c) ….. (2) 

Dividing (2) by (1) we get

Using (3) in (1) we get

(iii) xy = c²

Differentating w.r.t.x, we get,

xdy/dx + y = 0 is the required differential equation 

(iv) x² + y² = a²

Differentiating w.r.t.x, we get,

2x + 2y(dy/dx) = 0

(or) x + y(dy/dx) = 0 is the required differeantial equation.