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Miscellaneous

Misc 1 (i)

Misc 1 (ii)

Misc 1 (iii) Important

Misc 2 (i)

Misc 2 (ii) Important

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Misc 2 (iv) Important

Misc 3 Important

Misc 4

Misc 5 Important

Misc 6

Misc 7 Important

Misc 8 Important

Misc 9

Misc 10 Important

Misc 11

Misc 12 Important

Misc 13 (MCQ)

Misc 14 (MCQ) Important

Misc 15 (MCQ)

Question 1 Deleted for CBSE Board 2024 Exams

Question 2 Important Deleted for CBSE Board 2024 Exams

Question 3 Important Deleted for CBSE Board 2024 Exams

Chapter 9 Class 12 Differential Equations

Serial order wise

Last updated at Aug. 14, 2023 by Teachoo

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 . (iii) π¦=π₯ sinβ‘3π₯ : (π^2 π¦)/(ππ₯^2 )+9π¦β6 cosβ‘γ3π₯=0γ π¦=π₯ sinβ‘3π₯ Differentiating w.r.t x π¦^β²=(π₯ π ππβ‘3π₯ )^β² π¦^β²=π₯^β² sinβ‘3π₯+π₯(sinβ‘3π₯)β² π¦^β²=sinβ‘3π₯+π₯Γ3 cosβ‘3π₯ π^β²=πππβ‘ππ+ππ πππβ‘ππ Differentiating again w.r.t. x π¦^β²β²=(sinβ‘3π₯ )^β²+(3π₯ cosβ‘3π₯ )^β² π¦^β²β²=3 cosβ‘3π₯+γ3(π₯)γ^β² cosβ‘3π₯+3π₯ (cosβ‘3π₯ )^β² π¦^β²β²=3 cosβ‘3π₯+3 cosβ‘3π₯+3π₯(β3 sinβ‘3π₯) π^β²β²=π πππβ‘ππβππ πππβ‘ππ Putting π¦=π₯ sinβ‘3π₯ π¦^β²β²=6 cosβ‘3π₯β9π¦ π^β²β²+ππβπ πππβ‘ππ=π Thus, Given Function is a solution of the Differential Equation