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  1. Class 12
  2. Important Questions for exams Class 12

Transcript

Example 1 Find the order and degree, if defined , of each of the following differential equations : (i) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅโˆ’cosโกใ€–๐‘ฅ=0ใ€— ๐‘‘๐‘ฆ/๐‘‘๐‘ฅโˆ’cosโกใ€–๐‘ฅ=0ใ€— ๐‘ฆ^โ€ฒโˆ’cosโกใ€–๐‘ฅ=0ใ€— Highest order of derivative =1 โˆด Order = ๐Ÿ Degree = Power of ๐‘ฆ^โ€ฒ Degree = ๐Ÿ Example 1 Find the order and degree, if defined , of each of the following differential equations : (ii) ๐‘ฅ๐‘ฆ (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )+๐‘ฅ(๐‘‘๐‘ฆ/๐‘‘๐‘ฅ)^2โˆ’๐‘ฆ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=0 ๐‘ฅ๐‘ฆ (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )+๐‘ฅ(๐‘‘๐‘ฆ/๐‘‘๐‘ฅ)^2โˆ’๐‘ฆ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=0 ๐‘ฅ๐‘ฆ๐‘ฆ^โ€ฒโ€ฒ+๐‘ฅ(๐‘ฆ^โ€ฒ )^2โˆ’๐‘ฆ๐‘ฆ^โ€ฒ=0 Highest order of derivative = 2 โˆด Order = ๐Ÿ Degree = Power of ๐‘ฆ^โ€ฒโ€ฒ Degree = ๐Ÿ Example 1 Find the order and degree, if defined , of each of the following differential equations : (iii) ๐‘ฆ^โ€ฒโ€ฒโ€ฒ+๐‘ฆ^2+๐‘’^(๐‘ฆ^โ€ฒ )=0 ๐‘ฆ^โ€ฒโ€ฒโ€ฒ+๐‘ฆ^2+๐‘’^(๐‘ฆ^โ€ฒ )=0 Highest order of derivative = 3 โˆด Order = ๐Ÿ‘ Degree Since ๐‘ฆ^โ€ฒ is in ๐‘’^(๐‘ฆ^โ€ฒ ) It is not a polynomial equation โˆด 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.