Example 1 - Find order and degree of differential equations - Examples

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  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
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Example 1 Find the order and degree, if defined , of each of the following differential equations : (i) 𝑑𝑦﷮𝑑𝑥﷯− cos﷮𝑥=0﷯ 𝑑𝑦﷮𝑑𝑥﷯− cos﷮𝑥=0﷯ 𝑦﷮′﷯− cos﷮𝑥=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 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯+𝑥 𝑑𝑦﷮𝑑𝑥﷯﷯﷮2﷯−𝑦 𝑑𝑦﷮𝑑𝑥﷯=0 𝑥𝑦 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯+𝑥 𝑑𝑦﷮𝑑𝑥﷯﷯﷮2﷯−𝑦 𝑑𝑦﷮𝑑𝑥﷯=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﷮′′′﷯+ 𝑦﷮2﷯+ 𝑒﷮ 𝑦﷮′﷯﷯=0 𝑦﷮′′′﷯+ 𝑦﷮2﷯+ 𝑒﷮ 𝑦﷮′﷯﷯=0 Highest order of derivative =3 ∴ Order =𝟑 Degree Since 𝑦﷮′﷯ is in 𝑒﷮𝑦﷯′ It is not a polynomial equation in derivatives ∴ Degree is not defined

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