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Last updated at Dec. 11, 2019 by Teachoo

Transcript

Example 3 Verify that the function π¦=π cosβ‘γπ₯+π sinβ‘γπ₯, γ γ where , π, πβπ is a solution of the differential equation (π^2 π¦)/(ππ₯^2 )+π¦=0 π¦=π cosβ‘γπ₯+π sinβ‘γπ₯ γ γ ππ¦/ππ₯=π/ππ₯ (π cosβ‘γπ₯+π sinβ‘γπ₯ γ γ ) =π π(cosβ‘π₯ )/ππ₯+π π(sinβ‘π₯ )/ππ₯ =π(γβsinγβ‘π₯ )+π(cosβ‘π₯ ) =βπ π πππ₯+π πππ π₯ (π^2 π¦)/(ππ₯^2 )=π/ππ₯ (ππ¦/ππ₯) =π/ππ₯ (βπ π πππ₯+π πππ π₯) =βπ π(sinβ‘π₯ )/ππ₯+π (π(cosβ‘π₯))/ππ₯ =βπ(cosβ‘π₯ )+π(βsinβ‘π₯) =βπ cosβ‘γπ₯βπ sinβ‘π₯ γ Now, we have to verify (π^2 π¦)/(ππ₯^2 )+π¦=0 Taking L.H.S (π^2 π¦)/(ππ₯^2 )+π¦ =(βπ cosβ‘γπ₯βπ sinβ‘π₯ γ )+(π cosβ‘γπ₯+π sinβ‘π₯ γ ) =0 = R.H.S β΄ Hence Verified

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Example 3 You are here

Example 4 Not in Syllabus - CBSE Exams 2021

Example 5 Not in Syllabus - CBSE Exams 2021

Example 6 Important Not in Syllabus - CBSE Exams 2021

Example 7 Not in Syllabus - CBSE Exams 2021

Example 8 Not in Syllabus - CBSE Exams 2021

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Example 21 Not in Syllabus - CBSE Exams 2021

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Example 25 Not in Syllabus - CBSE Exams 2021

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Example 28 Important Not in Syllabus - CBSE Exams 2021

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