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Misc 3 - Form differential equation (x - a)2 + 2y2 = a2 - Miscellaneou

Misc 3 - Chapter 9 Class 12 Differential Equations - Part 2
Misc 3 - Chapter 9 Class 12 Differential Equations - Part 3

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Transcript

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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.