CBSE Class 12 Sample Paper for 2021 Boards

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Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Question 25 - CBSE Class 12 Sample Paper for 2021 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at December 16, 2024 by

Solve the following differential equation: 𝑑𝑦 𝑑π‘₯ = π‘₯ 3 π‘π‘œπ‘ π‘’π‘ 𝑦, 𝑔𝑖𝑣𝑒𝑛 π‘‘β„Žπ‘Žπ‘‘ 𝑦(0) = 0.

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Solve differential equation: dy/dx = x^3 cosec y, given that y(0) = 0

Question 25 - CBSE Class 12 Sample Paper for 2021 Boards - Part 2

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Transcript

Question 25 Solve the following differential equation: 𝑑𝑦/𝑑π‘₯ = π‘₯3 π‘π‘œπ‘ π‘’π‘ 𝑦, 𝑔𝑖𝑣𝑒𝑛 π‘‘β„Žπ‘Žπ‘‘ 𝑦(0) = 0. Given 𝑑𝑦/𝑑π‘₯ = π‘₯3 π‘π‘œπ‘ π‘’π‘ 𝑦 𝑑𝑦 Γ— 1/(π‘π‘œπ‘ π‘’π‘ 𝑦) = π‘₯3 𝑑π‘₯ 𝑑𝑦 Γ— sin y = π‘₯3 𝑑π‘₯ Integrating both sides ∫1β–’γ€–sin⁑𝑦 𝑑𝑦〗 = ∫1β–’γ€–π‘₯^3 𝑑π‘₯γ€— βˆ’π‘π‘œπ‘  𝑦 = π‘₯^4/4+𝐢 Since y(0) = 0 Putting x = 0, y = 0 βˆ’π‘π‘œπ‘  0 = 0/4+𝐢 βˆ’1 = 𝐢 π‘ͺ=βˆ’πŸ So, our equation becomes βˆ’π‘π‘œπ‘  𝑦 = π‘₯^4/4+𝐢 βˆ’π‘π‘œπ‘  𝑦 = π‘₯^4/4βˆ’1 𝒙^πŸ’/πŸ’+πœπ¨π¬β‘π’šβˆ’πŸ=𝟎

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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