Misc 9 - Find particular solution: (1 + e2x)dy + (1 + y2) ex - Variable separation - Equation given

Slide10.JPG
Slide11.JPG

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

Transcript

Misc 9 Find the particular solution of the differential equation (1 + 2 ) dy + (1 + 2 ) ex dx = 0, given that y = 1 when x = 0. (1 + e2x) dy + (1 + y2) dx = 0 (1 + e2x) dy = (1 + y2) dx = 1 + 2 . 1 + 2 1 + 2 = 1 + 2 Integrating both sides. 1 + 2 = 1 + 2 Let t = ex Diff w.r.t.x = = Our equation becomes 1 + 2 = 1 + 2 1 + 2 = 1 + 2 tan 1 y = tan 1 t+C Putting value of t tan 1 y = tan 1 ex + c Given that y = 1 when x = 0 Put y = 1 and x = 0 in (2) tan 1 (1) = tan 1 e + C 4 = tan 1 1+ 4 = 4 + C 4 + 4 = C C = 2 . Putting value of C in (1) tan 1 y = tan 1 ex 2 tan 1 y + tan 1 ex = is The required particular solution.

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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.