Exercise 4.1: Formation of ordinary differential equations

Exercise 4.1

1. Find the order and degree of the following differential equations.

2.   Find the differential equation of the following

(i) y = cx + c − c3   (ii) y = c ( x − c)2   (iii) xy = c2   (iv) x 2 + y2 = a2

3.  Form the differential equation by eliminating α and β (x-α)2+(y-β)2 = r2

4. Find the differential equation of the family of all straight lines passing through the origin.

5. Form the differential equation that represents all parabolas each of which has a latus rectum 4a and whose axes are parallel to the x axis.

6. Find the differential equation of all circles passing through the origin and having their centers on the y axis.

7. Find the differential equation of the family of parabola with foci at the origin and axis along the x-axis.