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Example 13 - Chapter 9 Class 12 Differential Equations (Term 2)
Last updated at Nov. 14, 2019 by Teachoo
Examples
Example 1 (i)
Example 1 (ii) Important
Example 1 (iii) Important
Example 2
Example 3 Important
Example 4 Deleted for CBSE Board 2023 Exams
Example 5 Deleted for CBSE Board 2023 Exams
Example 6 Important Deleted for CBSE Board 2023 Exams
Example 7 Deleted for CBSE Board 2023 Exams
Example 8 Deleted for CBSE Board 2023 Exams
Example 9
Example 10
Example 11
Example 12 Important
Example 13 You are here
Example 14 Important
Example 15 Important
Example 16
Example 17 Important
Example 18 Important
Example 19
Example 20 Important
Example 21
Example 22 Important
Example 23 Important
Example 24
Example 25 Deleted for CBSE Board 2023 Exams
Example 26
Example 27 Important
Example 28 Important
Chapter 9 Class 12 Differential Equations
Serial order wise
Transcript
Example 13 Find the equation of a curve passing through the point (β2 ,3), given that the slope of the tangent to the curve at any point (π₯ , π¦) is 2π₯/π¦^2 Slope of tangent = ππ¦/ππ₯ β΄ ππ¦/ππ₯ = 2π₯/π¦2 π¦2 dy = 2x dx Integrating both sides β«1βπ¦2 ππ¦= β«1βγ2π₯ ππ₯γ π¦^3/3 = 2.π₯^2/2 + C π¦^3/3 = π₯^2 + C π¦^3 = γ3π₯γ^2+3πΆ π¦^3 = γ3π₯γ^2+πΆ1 where πΆ1 = 3C Given that equation passes through (β2, 3) Putting x = β2, y = 3 in (1) y3 = 3x2 + C1 33 = 3(β2)2 + C1 27 = 3 Γ 4 + C1 27 β 12 = C1 15 = C1 C1 = 15 Putting C1 in (1) y3 = 3x2 + 15 y = "(3x2 + " γ"15)" γ^(π/π) " "is the particular solution of the equation.
