# Example 3 - Chapter 9 Class 12 Differential Equations

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 3 Verify that the function 𝑦=𝑎 cos𝑥+𝑏 sin𝑥, where , 𝑎, 𝑏∈𝐑 is a solution of the differential equation 𝑑2𝑦𝑑 𝑥2+𝑦=0 𝑦=𝑎 cos𝑥+𝑏 sin𝑥 𝑑𝑦𝑑𝑥= 𝑑𝑑𝑥 𝑎 cos𝑥+𝑏 sin𝑥 =𝑎 𝑑 cos𝑥𝑑𝑥+𝑏 𝑑 sin𝑥𝑑𝑥 =𝑎 −sin𝑥+𝑏 cos𝑥 =−𝑎 𝑠𝑖𝑛𝑥+𝑏 𝑐𝑜𝑠𝑥 𝑑2𝑦𝑑 𝑥2= 𝑑𝑑𝑥 𝑑𝑦𝑑𝑥 = 𝑑𝑑𝑥 −𝑎 𝑠𝑖𝑛𝑥+𝑏 𝑐𝑜𝑠𝑥 =−𝑎 𝑑 sin𝑥𝑑𝑥+𝑏 𝑑𝑑𝑥 cos𝑥 =−𝑎 cos𝑥+𝑏 − sin𝑥 =−𝑎 cos𝑥+𝑏− sin𝑥 Now , we have to verify 𝑑2𝑦𝑑 𝑥2+𝑦=0 Taking L.H.S 𝑑2𝑦𝑑 𝑥2+𝑦 = −𝑎 cos𝑥−𝑏− sin𝑥+ 𝑎 cos𝑥+𝑏 sin𝑥 =0 = R.H.S ∴ Hence Verified

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Chapter 9 Class 12 Differential Equations

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.