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Example 13 - Chapter 9 Class 12 Differential Equations
Last updated at Nov. 14, 2019 by Teachoo
Transcript
Example 13 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 ๐๐ฆ/๐๐ฅ = 2๐ฅ/๐ฆ2 ๐ฆ2 dy = 2x dx Integrating both sides โซ1โ๐ฆ2 ๐๐ฆ= โซ1โใ2๐ฅ ๐๐ฅใ ๐ฆ^3/3 = 2.๐ฅ^2/2 + C ๐ฆ^3/3 = ๐ฅ^2 + C ๐ฆ^3 = ใ3๐ฅใ^2+3๐ถ ๐ฆ^3 = ใ3๐ฅใ^2+๐ถ1 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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Important
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Example 4 Not in Syllabus - CBSE Exams 2021
Example 5 Not in Syllabus - CBSE Exams 2021
Example 6 Important Not in Syllabus - CBSE Exams 2021
Example 7 Not in Syllabus - CBSE Exams 2021
Example 8 Not in Syllabus - CBSE Exams 2021
Example 9
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Example 13 You are here
Example 14 Important
Example 15 Important
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Example 21 Not in Syllabus - CBSE Exams 2021
Example 22 Important
Example 23 Important
Example 24
Example 25 Not in Syllabus - CBSE Exams 2021
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Example 27 Important
Example 28 Important Not in Syllabus - CBSE Exams 2021
Chapter 9 Class 12 Differential Equations
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About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.