Ex 9.6, 3 - Find general solution: dy/dx + y/x = x2 - Ex 9.6

Slide8.JPG

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

Transcript

Ex 9.6, 3 For each of the differential equation given in Exercises 1 to 12, find the general solution : 𝑑𝑦﷮𝑑𝑥﷯+ 𝑦﷮𝑥﷯= 𝑥﷮2﷯ 𝑑𝑦﷮𝑑𝑥﷯+ 𝑦﷮𝑥﷯= 𝑥﷮2﷯ Differential equation is of the form 𝑑𝑦﷮𝑑𝑥﷯+𝑃𝑦=𝑄 where P = 1﷮𝑥﷯ and Q = x2 Finding integrating factor, I.F = e﷮ ﷮﷮𝑝 𝑑𝑥﷯﷯ IF = e﷮ ﷮﷮ 1﷮𝑥﷯ 𝑑𝑥﷯﷯ IF = e﷮ log﷮𝑥﷯﷯ IF = x Solution is y (IF) = ﷮﷮ 𝑄×𝐼𝐹﷯𝑑𝑥+𝑐﷯ yx = ﷮﷮ 𝑥﷮2﷯×𝑥×𝑑𝑥+𝑐﷯ yx = ﷮﷮ 𝑥﷮3﷯𝑑𝑥+𝑐﷯ yx = 𝑥﷮4﷯﷮4﷯+𝑐 xy = 𝒙﷮𝟒﷯﷮𝟒﷯+𝒄

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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/.
Jail