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  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise

Transcript

Misc 1 For each of the differential equation given below , indicate its order and degree (𝑖𝑓 𝑑𝑒𝑓𝑖𝑛𝑒𝑑) (i) (𝑑^2 𝑦)/(𝑑π‘₯^2 )+5π‘₯(𝑑𝑦/𝑑π‘₯)^2βˆ’6𝑦=log⁑π‘₯ (𝑑^2 𝑦)/(𝑑π‘₯^2 )+5π‘₯(𝑑𝑦/𝑑π‘₯)^2βˆ’6𝑦=log⁑π‘₯ 𝑦^β€²β€²+5π‘₯〖𝑦′〗^2βˆ’6𝑦=π‘™π‘œπ‘”β‘π‘₯ Highest order of derivative = 2 ∴ Order = 2 Since, power of y” is 1 ∴ Degree = 1 Misc 1 For each of the differential equation given below , indicate its order and degree (𝑖𝑓 𝑑𝑒𝑓𝑖𝑛𝑒𝑑) (ii) (𝑑𝑦/𝑑π‘₯)^3βˆ’4(𝑑𝑦/𝑑π‘₯)^2+7𝑦=sin⁑π‘₯ (𝑑𝑦/𝑑π‘₯)^3βˆ’4(𝑑𝑦/𝑑π‘₯)^2+7𝑦=sin⁑π‘₯ 𝑦^β€²3βˆ’4𝑦^β€²2+7𝑦=sin⁑π‘₯ Highest order of derivative = 1 Order = 1 Since, highest power of y’ is 3, Degree = 3 Misc 1 For each of the differential equation given below , indicate its order and degree (𝑖𝑓 𝑑𝑒𝑓𝑖𝑛𝑒𝑑) (iii) (𝑑^4 𝑦)/(𝑑π‘₯^4 )βˆ’π‘ π‘–π‘›((𝑑^3 𝑦)/(𝑑π‘₯^3 ))=0 (𝑑^4 𝑦)/(𝑑π‘₯^4 )βˆ’π‘ π‘–π‘›((𝑑^3 𝑦)/(𝑑π‘₯^3 ))=0 𝑦^β€²β€²β€²β€²βˆ’π‘ π‘–π‘› (𝑦^β€²β€²β€² )=0 Highest order of derivative = 4 ∴ Order = 4 Since 𝑦^β€²β€²β€² is in sin (y^β€²β€²β€² ) It is not a polynomial equation Thus, degree is not defined.

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.