# Question 6 - Examples - Chapter 9 Class 12 Differential Equations

Last updated at April 16, 2024 by Teachoo

Examples

Example 1 (i)

Example 1 (ii) Important

Example 1 (iii) Important

Example 2

Example 3 Important

Example 4

Example 5

Example 6

Example 7 Important

Example 8

Example 9 Important

Example 10 Important

Example 11

Example 12 Important

Example 13 Important

Example 14

Example 15 Important

Example 16

Example 17 Important

Example 18 Important

Example 19

Example 20

Example 21 Important

Example 22 Important

Question 1 Deleted for CBSE Board 2025 Exams

Question 2 Deleted for CBSE Board 2025 Exams

Question 3 Important Deleted for CBSE Board 2025 Exams

Question 4 Deleted for CBSE Board 2025 Exams

Question 5 Deleted for CBSE Board 2025 Exams

Question 6 Deleted for CBSE Board 2025 Exams You are here

Chapter 9 Class 12 Differential Equations

Serial order wise

Last updated at April 16, 2024 by Teachoo

Question 6 From the differential equation of the family of circles in the second quadrant and touching the coordinate axes . Drawing figure : Let C be the family of circles in second quadrant touching coordinate. Let radius be 𝑎 ∴ Center of circle = (−𝑎, 𝑎) Equation representing family C is x−(−𝑎)2+ 𝑦−𝑎2= 𝑎2 x + 𝑎2+ 𝑦−𝑎2= 𝑎2 𝑥2 + 𝑎2 + 2ax + y2 + 𝑎2 − 2𝑎y = 𝑎2 𝑥2 + 𝑦2 + 2ax − 2ay + 2𝑎2 = 𝑎2 𝑥2 + y2 + 2𝑎x − 2𝑎y + 𝑎2 = 0 Differentiate w.r.t x 2x + 2y. 𝑑𝑦𝑑𝑥 + 2𝑎 − 2a 𝑑𝑦𝑑𝑥 + 0 = 0 x + y. 𝑑𝑦𝑑𝑥 + 𝑎 − 𝑎𝑑𝑦𝑑𝑥 = 0 x + y. 𝑑𝑦𝑑𝑥 = − 𝑎 + 𝑎𝑑𝑦𝑑𝑥 x + y 𝑑𝑦𝑑𝑥 = 𝑎 𝑑𝑦𝑑𝑥 −1 𝑎 = 𝑥 + 𝑦 𝑑𝑦𝑑𝑥 𝑑𝑦𝑑𝑥 − 1 𝑎 = 𝒙 + 𝒚 𝒚′ 𝒚′ − 𝟏 Putting value of a in (1) x−(−𝑎)2+ 𝑦−𝑎2= 𝑎2 x− − 𝑥 + 𝑦 𝑦′ 𝑦′ − 12+ 𝑦− 𝑥 + 𝑦 𝑦′ 𝑦′ − 12= 𝑥 + 𝑦 𝑦′ 𝑦′ − 12 x+ 𝑥 + 𝑦 𝑦′ 𝑦′ − 12+ 𝑦− 𝑥 + 𝑦 𝑦′ 𝑦′ − 12= 𝑥 + 𝑦 𝑦′ 𝑦′ − 12 𝑥 𝑦′− 1 + 𝑥 + 𝑦 𝑦′ 𝑦′ − 12+ 𝑦 𝑦′− 1 − 𝑥 − 𝑦 𝑦′ 𝑦′ − 12= 𝑥 + 𝑦 𝑦′ 𝑦′ − 12 𝑥 𝑦′ − 𝑥 + 𝑥 + 𝑦 𝑦′ 𝑦′ − 12+ −𝑥 − 𝑦 𝑦′ − 12= 𝑥 + 𝑦 𝑦′ 𝑦′ − 12 (𝑥 + 𝑦) 𝑦′ 𝑦′ − 12+ −(𝑥 + 𝑦) 𝑦′ − 12= 𝑥 + 𝑦 𝑦′ 𝑦′ − 12 (𝑥 + 𝑦) 2 ( 𝑦′)2+ (𝑥 + 𝑦) 2= 𝑥 + 𝑦 𝑦′2 (𝒙 + 𝒚) 𝟐 ( 𝒚′)𝟐 + 𝟏= 𝒙 + 𝒚 𝒚′𝟐 which is the required differential equation