# Misc 18 - Chapter 9 Class 12 Differential Equations

Last updated at Dec. 11, 2019 by Teachoo

Last updated at Dec. 11, 2019 by Teachoo

Transcript

Misc 18 The general solution of the differential equation π^π₯ ππ¦+(π¦ π^π₯+2π₯)ππ₯=0 is (A) π₯ π^π¦+π₯^2=πΆ (B) π₯ π^π¦+π¦^2=πΆ (C) π¦ π^π₯+π₯^2=πΆ (D) π¦ π^π¦+π₯^2=πΆ Given equation π^π₯ ππ¦+(π¦ π^π₯+2π₯)ππ₯=0 π^π₯ ππ¦=β(π¦ π^π₯+2π₯)ππ₯ ππ¦/ππ₯= (β(π¦π^π₯ + 2π₯))/π^π₯ ππ¦/ππ₯ = (βπ¦π^π₯)/π^π₯ β2π₯/π^π₯ ππ¦/ππ₯ = βπ¦β2π₯/π^π₯ ππ¦/ππ₯ + y = (β2π₯)/π^π₯ Differential equation is of the form ππ¦/ππ₯ + Py = Q where P = 1 & Q = (β2π₯)/π^π₯ IF = π^β«1βγπ ππ₯γ IF = π^β«1βγ1 ππ₯γ IF = π^π₯ Solution is y(IF) = β«1βγ(πΓπΌπΉ)ππ₯+πγ yex = β«1βγ(β2π₯)/π^π₯ π^π₯ ππ₯+πγ yex = ββ«1βγ2π₯ ππ₯+πγ yex = β2Γπ₯^2/2+π yex = βπ₯^2+π yex + π₯^2=π β΄ Option (C) is the correct answer

Miscellaneous

Misc 1
Important

Misc 2 Important

Misc 3 Deleted for CBSE Board 2022 Exams

Misc 4 Important

Misc 5 Important Deleted for CBSE Board 2022 Exams

Misc 6

Misc 7 Important

Misc 8

Misc 9 Important

Misc 10 Important

Misc 11

Misc 12

Misc 13

Misc 14 Important

Misc 15 Important

Misc 16

Misc 17 Important Deleted for CBSE Board 2022 Exams

Misc 18 You are here

Chapter 9 Class 12 Differential Equations (Term 2)

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 10 years. He provides courses for Maths and Science at Teachoo.