Example 3 - Chapter 9 Class 12 Differential Equations
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
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 π π/π π=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 ππππ+π ππππ Now, (π^2 π¦)/(ππ₯^2 )=π/ππ₯ (ππ¦/ππ₯) (π ^π π)/(π π^π ) =π /π π (βπ ππππ+π ππππ) (π^2 π¦)/(ππ₯^2 ) =βπ π(sinβ‘π₯ )/ππ₯+π (π(cosβ‘π₯))/ππ₯ (π^2 π¦)/(ππ₯^2 ) =βπ(cosβ‘π₯ )+π(βsinβ‘π₯) (π^2 π¦)/(ππ₯^2 ) =βπ πππ β‘γπ₯βπ π ππβ‘π₯ γ (π ^π π)/(π π^π ) =β(π πππβ‘γπ+π πππβ‘π γ ) Putting y = π cosβ‘γπ₯+π sinβ‘γπ₯ γ γ (π ^π π)/(π π^π )=βπ (π ^π π)/(π π^π )+π=π β΄ Hence Verified
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo