Example 3 - Chapter 9 Class 12 Differential Equations
Last updated at April 16, 2024 by Teachoo
Gen and Particular Solution
Ex 9.2, 12 (MCQ) Important
Question 11 (MCQ) Deleted for CBSE Board 2024 Exams
Question 12 (MCQ) Important Deleted for CBSE Board 2024 Exams
Example 2
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Example 3 Important You are here
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Example 19
Misc 2 (i)
Gen and Particular Solution
Last updated at April 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