Miscellaneous

Chapter 9 Class 12 Differential Equations
Serial order wise

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### Transcript

Misc 2 For each of the exercise given below , verify that the given function (ππππππππ‘ ππ ππ₯ππππππ‘) is a solution of the corresponding differential equation . (iii) π¦=π₯ sinβ‘3π₯ : (π^2 π¦)/(ππ₯^2 )+9π¦β6 cosβ‘γ3π₯=0γ π¦=π₯ sinβ‘3π₯ Differentiating w.r.t x π¦^β²=(π₯ π ππβ‘3π₯ )^β² π¦^β²=π₯^β² sinβ‘3π₯+π₯(sinβ‘3π₯)β² π¦^β²=sinβ‘3π₯+π₯Γ3 cosβ‘3π₯ π¦^β²=sinβ‘3π₯+3π₯ cosβ‘3π₯ Differentiating again w.r.t. x π¦^β²β²=(sinβ‘3π₯ )^β²+(3π₯ cosβ‘3π₯ )^β² π¦^β²β²=3 cosβ‘3π₯+γ3(π₯)γ^β² cosβ‘3π₯+3π₯ (cosβ‘3π₯ )^β² π¦^β²β²=3 cosβ‘3π₯+3 cosβ‘3π₯+3π₯(β3 sinβ‘3π₯) π¦^β²β²=6 cosβ‘3π₯β9π₯ sinβ‘3π₯ Putting π¦=π₯ sinβ‘3π₯ π¦^β²β²=6 cosβ‘3π₯β9π¦ π¦^β²β²+9π¦β6 cosβ‘3π₯=0 Thus, Given Function is a solution of the Differential Equation