# Misc 2 (iv) - Chapter 9 Class 12 Differential Equations (Term 2)

Last updated at Aug. 20, 2021 by

Last updated at Aug. 20, 2021 by

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Misc 2 For each of the exercise given below , verify that the given function (ππππππππ‘ ππ ππ₯ππππππ‘) is a solution of the corresponding differential equation . (iv) π₯^2=2π¦^2 logβ‘π¦ : (π₯^2+π¦^2 ) ππ¦/ππ₯βπ₯π¦=0 π₯^2=2π¦^2 logβ‘π¦ Differentiating Both sides w.r.t. x (π₯^2 )^β²=(2π¦^2 logβ‘π¦ )β² 2π₯=(2π¦^2 )^β² logβ‘π¦ +2π¦^2 (logβ‘π¦ )^β² 2π₯=2Γ2π¦π¦^β² logβ‘π¦ + 2π¦^2Γ 1/π¦ π¦β² 2π₯=4π¦π¦^β² logβ‘π¦ + 2π¦π¦β² π₯=2π¦π¦^β² logβ‘π¦ + π¦π¦β² π₯=γπ¦π¦γ^β² (2 logβ‘π¦+1) Now, from our equation π₯^2=2π¦^2 logβ‘π¦ π₯^2/(2π¦^2 )=logβ‘π¦ πππβ‘π¦=π₯^2/(2π¦^2 ) Putting value of πππβ‘π¦ in (1) π₯=γπ¦π¦γ^β² (2 πππβ‘π+1) π₯=γπ¦π¦γ^β² (2Γπ₯^2/(2π¦^2 ) " " +1) π₯=γπ¦π¦γ^β² (π₯^2/π¦^2 " " +1) π₯=γπ¦π¦γ^β² ((π₯^2 + π¦^2)/π¦^2 ) π₯=π¦^β² ((π₯^2 + π¦^2)/π¦) π₯π¦=π¦^β² (π₯^2 + π¦^2 ) π¦^β² (π₯^2 + π¦^2 )βπ₯π¦=0 Thus, Given Function is a solution of the Differential Equation

Miscellaneous

Misc 1 (i)

Misc 1 (ii)

Misc 1 (iii) Important

Misc 2 (i)

Misc 2 (ii) Important

Misc 2 (iii)

Misc 2 (iv) Important You are here

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 Important

Misc 13

Misc 14 Important

Misc 15 Important

Misc 16 (MCQ)

Misc 17 (MCQ) Important Deleted for CBSE Board 2022 Exams

Misc 18 (MCQ)

Chapter 9 Class 12 Differential Equations (Term 2)

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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.