# Example 6 - Chapter 9 Class 12 Differential Equations (Term 2)

Last updated at Dec. 11, 2019 by

Last updated at Dec. 11, 2019 by

Transcript

Example 6 Form the differential equation representing the family of ellipses having foci on π₯βππ₯ππ is center at the origin. Ellipse whose foci is on x-axis & center at origin is π₯^2/π^2 +π¦^2/π^2 =1 Differentiating both sides w.r.t. π₯ π/ππ₯ [π₯^2/π^2 +π¦^2/π^2 ]=π(1)/ππ₯ 1/π^2 Γ(γπ(π₯γ^2))/ππ₯+1/π^2 Γ(γπ(π¦γ^2))/ππ₯=0 Since it has two variables, we will differentiate twice π₯^2/π^2 +π¦^2/π^2 =1 1/π^2 Γ2π₯+1/π^2 Γ(2π¦ . ππ¦/ππ₯)=0 2π₯/π^2 +2π¦/π^2 ππ¦/ππ₯=0 2π¦/π^2 ππ¦/ππ₯=(β2π₯)/γ πγ^2 π¦/π^2 ππ¦/ππ₯=(βπ₯)/γ πγ^2 π¦/π₯ ππ¦/ππ₯= (βπ^2)/γ πγ^2 π¦/π₯ π¦^β²= (βπ^2)/γ πγ^2 Again differentiating both sides π(π¦/π₯)/ππ₯. π¦^β²+π¦/π₯ (π(π¦^β²))/ππ₯=π/ππ₯ ((β π^2)/( π^2 )) [ππ¦/ππ₯ . π₯ β π¦ .ππ₯/ππ₯]/π₯^2 π¦^β² +π¦/π₯ Γπ¦β²β²=0 [π¦^β² π₯ β π¦]/π₯^2 π¦^β² +π¦/π₯Γπ¦β²β²=0 Multiplying x2 both sides π₯^2Γ[π¦^β² π₯ β π¦]/π₯^2 π¦^β² +π₯^2Γπ¦/π₯Γπ¦β²β²=π₯^2Γ0 [π¦^β² π₯βπ¦] π¦^β²+π₯π¦π¦^β²β²=0 γγπ₯π¦γ^β²γ^2βπ¦π¦^β²+π₯π¦π¦^β²β²=0 π₯π¦π¦^β²β²+γγπ₯π¦γ^β²γ^2βπ¦π¦^β²=0 ππ (π ^π π)/(π π^π ) +π(π π/π π)^πβπ π π/π π=π is the required differential equation

Examples

Example 1 (i)

Example 1 (ii) Important

Example 1 (iii) Important

Example 2

Example 3 Important

Example 4 Deleted for CBSE Board 2022 Exams

Example 5 Deleted for CBSE Board 2022 Exams

Example 6 Important Deleted for CBSE Board 2022 Exams You are here

Example 7 Deleted for CBSE Board 2022 Exams

Example 8 Deleted for CBSE Board 2022 Exams

Example 9

Example 10

Example 11

Example 12 Important

Example 13

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Example 17 Important

Example 18 Important

Example 19

Example 20 Important

Example 21 Deleted for CBSE Board 2022 Exams

Example 22 Important

Example 23 Important

Example 24

Example 25 Deleted for CBSE Board 2022 Exams

Example 26

Example 27 Important

Example 28 Important Deleted for CBSE Board 2022 Exams

Chapter 9 Class 12 Differential Equations (Term 2)

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.