Example 8 - Chapter 9 Class 12 Differential Equations
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 8 Find the equation of a curve passing through the point (โ2 ,3), given that the slope of the tangent to the curve at any point (๐ฅ , ๐ฆ) is 2๐ฅ/๐ฆ^2 Slope of tangent = ๐๐ฆ/๐๐ฅ โด ๐ ๐/๐ ๐ = ๐๐/๐๐ ๐ฆ2 dy = 2x dx Integrating both sides โซ1โ๐๐ ๐ ๐= โซ1โใ๐๐ ๐ ๐ใ ๐ฆ^3/3 = 2.๐ฅ^2/2 + C ๐ฆ^3/3 = ๐ฅ^2 + C ๐ฆ^3 = ใ3๐ฅใ^2+3๐ถ ๐^๐ = ใ๐๐ใ^๐+๐ช๐ where ๐ถ1 = 3C Given that equation passes through (โ2, 3) Putting x = โ2, y = 3 in (1) y3 = 3x2 + C1 33 = 3(โ2)2 + C1 27 = 3 ร 4 + C1 27 โ 12 = C1 15 = C1 C1 = 15 Putting C1 in (1) y3 = 3x2 + 15 y = "(3x2 + " ใ"15)" ใ^(๐/๐) " "is the particular solution of the equation.
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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