# Misc 3 - Chapter 9 Class 12 Differential Equations (Term 2)

Last updated at Dec. 11, 2019 by Teachoo

Miscellaneous

Misc 1 (i)

Misc 1 (ii)

Misc 1 (iii) Important

Misc 2 (i)

Misc 2 (ii) Important

Misc 2 (iii)

Misc 2 (iv) Important

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Misc 4 Important

Misc 5 Important Deleted for CBSE Board 2022 Exams

Misc 6

Misc 7 Important

Misc 8

Misc 9 Important

Misc 10 Important

Misc 11

Misc 12 Important

Misc 13

Misc 14 Important

Misc 15 Important

Misc 16 (MCQ)

Misc 17 (MCQ) Important Deleted for CBSE Board 2022 Exams

Misc 18 (MCQ)

Chapter 9 Class 12 Differential Equations (Term 2)

Serial order wise

Last updated at Dec. 11, 2019 by Teachoo

Misc 3 From the differential equation representing the family of curves given by (𝑥−𝑎)^2+2𝑦^2=𝑎^2, where 𝑎 is an arbitrary constant (𝑥−𝑎)^2+2𝑦^2=𝑎^2 Differentiating w.r.t. 𝑥 〖[(𝑥−𝑎)^2]〗^′+(2𝑦^2 )^′=(𝑎^2 )^′ 2(𝑥−𝑎)+2×2𝑦𝑦^′=0 (𝑥−𝑎)+2𝑦𝑦^′=0 𝑥+2𝑦𝑦^′=𝑎 𝑎=𝑥+2〖𝑦𝑦〗^′ Since it has one variable, we will differentiate once a = 2𝑦 𝑑𝑦/𝑑𝑥+𝑥 Putting value of a in (𝑥−𝑎)^2+2𝑦^2=𝑎^2 [𝑥−(𝑥+2𝑦𝑦^′)]^2+2𝑦^2=〖(𝑥+2𝑦𝑦^′)〗^2 (−2𝑦𝑦^′ )^2+2𝑦^2=〖(𝑥+2𝑦𝑦^′)〗^2 4𝑦^2 〖𝑦^′〗^2+2𝑦^2=𝑥^2+4𝑦^2 〖𝑦^′〗^2+4𝑥𝑦𝑦^′ 2𝑦^2=𝑥^2+4𝑥𝑦𝑦^′ 2𝑦^2−𝑥^2=4𝑥𝑦𝑦^′ (2𝑦^2− 𝑥^2)/4𝑥𝑦=𝑦^′ 𝒚^′=(𝟐𝒚^𝟐 − 𝒙^𝟐)/𝟒𝒙𝒚