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The differential equation of all circles which passes through the origin and whose centre lies on y axis is

The differential equation of all circles which passes through the origin and whose centre lies on y axis is

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear pallavi

let the center is (o,a)  and  radius is r

so equation of circle is

x2 + (y-a)2 =r2

 differentiate

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

x+ (y-a)dy/dx =0  ..............1

 

again differentiate

1+ (y-a)d2y/dx2 + dy/dx =0

put value of (y-a) from equation 1

1 -x(d2y/dx2)/(dy/dx) + dy/dx =0

(dy/dx )2 + dy/dx  - xd2y/dx2=0

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