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 2024 Exams

Question 2 Deleted for CBSE Board 2024 Exams

Question 3 Important Deleted for CBSE Board 2024 Exams

Question 4 Deleted for CBSE Board 2024 Exams You are here

Question 5 Deleted for CBSE Board 2024 Exams

Question 6 Deleted for CBSE Board 2024 Exams

Chapter 9 Class 12 Differential Equations

Serial order wise

Last updated at April 16, 2024 by Teachoo

Question 4 Form the differential equation of the family of circles touching the x-axis at origin. We know that, Equation of Circle is (𝑥−𝑎)^2+(𝑦−𝑏)^2=𝑟^2 Center =(𝑎,𝑏) Radius = 𝑟 Since the circle touches the x-axis at origin The center will be on the y-axis So, x-coordinate of center is 0 i.e. a = 0 ∴ Center = (0 , 𝑏) And, 𝑟𝑎𝑑𝑖𝑢𝑠=𝑏 So, Equation of Circle (𝑥−0)^2+(𝑦−𝑏)^2=𝑏^2 𝑥^2+(𝑦−𝑏)^2=𝑏^2 𝑥^2+𝑦^2−2𝑦𝑏+𝑏^2=𝑏^2 𝑥^2+𝑦^2−2𝑦𝑏=0 𝑥^2+𝑦^2=2𝑦𝑏 Since there is one variable b, we differentiate once Diff. w.r.t. 𝑥 2𝑥+2𝑦 𝑑𝑦/𝑑𝑥=2𝑏.𝑑𝑦/𝑑𝑥 𝑥+𝑦𝑦^′=𝑏.𝑦′ [(𝑥 + 𝑦𝑦^′)/𝑦^′ ]=𝑏 Putting Value of 𝑏 in (1) 𝑥^2+𝑦^2=2𝑦[(𝑥 + 𝑦𝑦^′)/𝑦^′ ] (𝑥^2+𝑦^2 ) 𝑦^′=2𝑦(𝑥+𝑦𝑦^′ ) (𝑥^2+𝑦^2 ) 𝑦^′=2𝑦𝑥+2𝑦^2 𝑦^′ 𝑥^2 𝑦^′+𝑦^2 𝑦^′=2𝑦𝑥+2𝑦^2 𝑦^′ 𝑥^2 𝑦^′+𝑦^2 𝑦^′−2𝑦^2 𝑦^′=2𝑦𝑥 𝑥^2 𝑦^′−𝑦^2 𝑦^′=2𝑦𝑥 𝑦^′ (𝑥^2−𝑦^2 )=2𝑥𝑦 𝐲′=𝟐𝒙𝒚/(𝒙^𝟐 − 𝒚^𝟐 )