# Misc 10 - Class 12

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc 10 Solve the differential equation 𝑦 𝑒 𝑥𝑦 𝑑𝑥= 𝑒 𝑥𝑦+ 𝑦2𝑑𝑦 𝑦≠0 𝑦 𝑒 𝑥𝑦 𝑑𝑥= 𝑒 𝑥𝑦+ 𝑦2𝑑𝑦 𝑑𝑦𝑑𝑥 = 𝑦 𝑒 𝑥𝑦𝑥 𝑒 𝑥𝑦 + 𝑦2 𝑑𝑥𝑑𝑦 = 𝑥 𝑒 𝑥𝑦 + 𝑦2 𝑦 𝑒 𝑥𝑦 𝑦 𝑒 𝑥𝑦 𝑑𝑥𝑑𝑦 = x 𝑒 𝑥𝑦 + y2 e 𝑥𝑦 y 𝑑𝑦 𝑥𝑑𝑦 − x 𝑒 𝑥𝑦 = y2 e 𝑥𝑦 y 𝑑𝑥𝑑𝑦 −x = y2 𝑒 𝑥𝑦 𝑦 𝑑𝑥𝑑𝑦 − 𝑥 𝑦2=1 Let 𝑒 𝑥𝑦 = z Diff w.r.t. y. 𝑒 𝑥𝑦 𝑑𝑑𝑦 𝑥𝑦= 𝑑𝑧𝑑𝑦 𝑒 𝑥𝑦 𝑦 𝑑𝑥𝑑𝑦 − 𝑥 𝑦2= 𝑑𝑧𝑑𝑦 From (1) 𝑑𝑧𝑑𝑦 = 1 dz = dy Integrating on both sides 𝑑𝑧 = 𝑑𝑦 z = y + c Putting 𝑒 𝑥𝑦 = z 𝒆 𝒙𝒚 = y + c

Chapter 9 Class 12 Differential Equations

Serial order wise

About the Author

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.