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Miscellaneous
Misc 1 (ii)
Misc 1 (iii) Important
Misc 2 (i)
Misc 2 (ii) Important
Misc 2 (iii)
Misc 2 (iv) Important
Misc 3 Deleted for CBSE Board 2023 Exams
Misc 4 Important
Misc 5 Important Deleted for CBSE Board 2023 Exams
Misc 6
Misc 7 Important
Misc 8
Misc 9 Important
Misc 10 Important
Misc 11
Misc 12 Important
Misc 13 You are here
Misc 14 Important
Misc 15 Important
Misc 16 (MCQ)
Misc 17 (MCQ) Important
Misc 18 (MCQ)
Last updated at Nov. 14, 2019 by Teachoo
Maths Crash Course - Live lectures + all videos + Real time Doubt solving!
Misc 13 Find a particular solution of the differential equation 𝑑𝑦𝑑𝑥+𝑦 cot𝑥=4𝑥 𝑐𝑜𝑠𝑒𝑐 𝑥 𝑥≠0 , given that 𝑦=0 when 𝑥= 𝜋2 Given 𝑑𝑦𝑑𝑥+𝑦 cot𝑥=4𝑥 𝑐𝑜𝑠𝑒𝑐 𝑥 This of the form 𝑑𝑦𝑑𝑥+𝑃𝑦=𝑄 where P = cot x & Q = 4x cosec x IF = 𝑒 𝑃𝑑𝑥 IF = 𝑒 cot𝑥 𝑑𝑥 IF = 𝑒log( sin𝑥) IF = sin x Solution is y (IF) = 𝑄×𝐼.𝐹𝑑𝑥+𝑐 y sin x = 4𝑥 𝑐𝑜𝑠𝑒𝑐 𝑥 sin𝑥 𝑑𝑥+𝑐 y sin x = 4𝑥 1 sin𝑥 sin𝑥𝑑𝑥+𝑐 y sin x = 4𝑥 𝑑𝑥+𝑐 y sin x = 4 𝑥22+𝑐 y sin x = 2x2 + C Given that 𝑦=0 when 𝑥= 𝜋2 Put x = 𝜋2 & y = 0 in (1) 0 × sin 𝜋2 = 2 𝜋22+𝐶 0 = 2 𝜋42 + C 0 = 𝜋22 + C C = −𝜋22 Putting value of C in (1) y sin x = 2x2 + c y sin x = 2 𝒙𝟐 − 𝝅𝟐𝟐