Example 1
Last updated at March 11, 2017 by Teachoo
Transcript
Example 1 Find the order and degree, if defined , of each of the following differential equations : (i) 𝑑𝑦𝑑𝑥− cos𝑥=0 𝑑𝑦𝑑𝑥− cos𝑥=0 𝑦′− cos𝑥=0 Highest order of derivative =1 ∴ Order =𝟏 Degree = Power of 𝑦′ Degree =𝟏 Example 1 Find the order and degree, if defined , of each of the following differential equations : (ii) 𝑥𝑦 𝑑2𝑦𝑑 𝑥2+𝑥 𝑑𝑦𝑑𝑥2−𝑦 𝑑𝑦𝑑𝑥=0 𝑥𝑦 𝑑2𝑦𝑑 𝑥2+𝑥 𝑑𝑦𝑑𝑥2−𝑦 𝑑𝑦𝑑𝑥=0 𝑥𝑦 𝑦′′+𝑥 𝑦′2+𝑦 𝑦′=0 Highest order of derivative =2 ∴ Order =𝟐 Degree = Power of 𝑦′′ Degree =𝟏 Example 1 Find the order and degree, if defined , of each of the following differential equations : (iii) 𝑦′′′+ 𝑦2+ 𝑒 𝑦′=0 𝑦′′′+ 𝑦2+ 𝑒 𝑦′=0 Highest order of derivative =3 ∴ Order =𝟑 Degree Since 𝑦′ is in 𝑒𝑦′ It is not a polynomial equation in derivatives ∴ Degree is not defined
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Chapter 9 Class 12 Differential Equations
Serial order wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.