# Question 3 - 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 You are here

Question 4 Deleted for CBSE Board 2025 Exams

Question 5 Deleted for CBSE Board 2025 Exams

Question 6 Deleted for CBSE Board 2025 Exams

Chapter 9 Class 12 Differential Equations

Serial order wise

Last updated at April 16, 2024 by Teachoo

Question 3 Form the differential equation representing the family of ellipses having foci on 𝑥−𝑎𝑥𝑖𝑠 is center at the origin. Ellipse whose foci is on x-axis & center at origin is 𝑥^2/𝑎^2 +𝑦^2/𝑏^2 =1 Differentiating both sides w.r.t. 𝑥 𝑑/𝑑𝑥 [𝑥^2/𝑎^2 +𝑦^2/𝑏^2 ]=𝑑(1)/𝑑𝑥 1/𝑎^2 ×(〖𝑑(𝑥〗^2))/𝑑𝑥+1/𝑏^2 ×(〖𝑑(𝑦〗^2))/𝑑𝑥=0 Since it has two variables, we will differentiate twice 𝑥^2/𝑎^2 +𝑦^2/𝑏^2 =1 1/𝑎^2 ×2𝑥+1/𝑏^2 ×(2𝑦 . 𝑑𝑦/𝑑𝑥)=0 2𝑥/𝑎^2 +2𝑦/𝑏^2 𝑑𝑦/𝑑𝑥=0 2𝑦/𝑏^2 𝑑𝑦/𝑑𝑥=(−2𝑥)/〖 𝑎〗^2 𝑦/𝑏^2 𝑑𝑦/𝑑𝑥=(−𝑥)/〖 𝑎〗^2 𝑦/𝑥 𝑑𝑦/𝑑𝑥= (−𝑏^2)/〖 𝑎〗^2 𝑦/𝑥 𝑦^′= (−𝑏^2)/〖 𝑎〗^2 Again differentiating both sides 𝑑(𝑦/𝑥)/𝑑𝑥. 𝑦^′+𝑦/𝑥 (𝑑(𝑦^′))/𝑑𝑥=𝑑/𝑑𝑥 ((− 𝑏^2)/( 𝑎^2 )) [𝑑𝑦/𝑑𝑥 . 𝑥 − 𝑦 .𝑑𝑥/𝑑𝑥]/𝑥^2 𝑦^′ +𝑦/𝑥 ×𝑦′′=0 [𝑦^′ 𝑥 − 𝑦]/𝑥^2 𝑦^′ +𝑦/𝑥×𝑦′′=0 Multiplying x2 both sides 𝑥^2×[𝑦^′ 𝑥 − 𝑦]/𝑥^2 𝑦^′ +𝑥^2×𝑦/𝑥×𝑦′′=𝑥^2×0 [𝑦^′ 𝑥−𝑦] 𝑦^′+𝑥𝑦𝑦^′′=0 〖〖𝑥𝑦〗^′〗^2−𝑦𝑦^′+𝑥𝑦𝑦^′′=0 𝑥𝑦𝑦^′′+〖〖𝑥𝑦〗^′〗^2−𝑦𝑦^′=0 𝒙𝒚 (𝒅^𝟐 𝒚)/(𝒅𝒙^𝟐 ) +𝒙(𝒅𝒚/𝒅𝒙)^𝟐−𝒚 𝒅𝒚/𝒅𝒙=𝟎 is the required differential equation