Example 7 - Chapter 9 Class 12 Differential Equations

Last updated at April 16, 2024 by

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Transcript

Example 7 Find the equation of the curve passing through the point (1 , 1) whose differential equation is 𝑥 𝑑𝑦= (2𝑥^2+1)𝑑𝑥(𝑥≠0) 𝑥 𝑑𝑦 = (2x2 + 1)dx dy = "(2x2 + 1)" /𝑥 dx dy = ("2x2" /𝑥+1/𝑥) dx dy = (𝟐𝒙+𝟏/𝒙) dx Integrating both sides. ∫1▒𝑑𝑦 = ∫1▒(2𝑥+1/𝑥) 𝑑𝑥 ∫1▒𝑑𝑦 = ∫1▒〖2𝑥 𝑑𝑥+〗 ∫1▒〖1/𝑥 𝑑𝑥〗 y = 2 𝑥2/2 + log |𝑥| + C y = 𝒙𝟐 + log |𝒙| + C Since the curve passes through point (1, 1) Putting x = 1, y = 1 is (1) 1 = 12 + log |𝟏| + C 1 = 1 + 0 + C 1 − 1 = C ∴ C = 0 Put C = 0 in (1) y = x2 + log |𝑥| + C y = x2 + log |𝒙| + 0 y = x2 + log |𝑥| Hence, the equation of curve is y = x2 + log |𝒙|

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.