Check sibling questions

Example 13 - Find curve (-2 ,3), slope of tangent is 2x/y2 - Examples

Example 13 - Chapter 9 Class 12 Differential Equations - Part 2


Transcript

Example 13 Find the equation of a curve passing through the point (βˆ’2 ,3), given that the slope of the tangent to the curve at any point (π‘₯ , 𝑦) is 2π‘₯/𝑦^2 Slope of tangent = 𝑑𝑦/𝑑π‘₯ ∴ 𝑑𝑦/𝑑π‘₯ = 2π‘₯/𝑦2 𝑦2 dy = 2x dx Integrating both sides ∫1▒𝑦2 𝑑𝑦= ∫1β–’γ€–2π‘₯ 𝑑π‘₯γ€— 𝑦^3/3 = 2.π‘₯^2/2 + C 𝑦^3/3 = π‘₯^2 + C 𝑦^3 = γ€–3π‘₯γ€—^2+3𝐢 𝑦^3 = γ€–3π‘₯γ€—^2+𝐢1 where 𝐢1 = 3C Given that equation passes through (βˆ’2, 3) Putting x = βˆ’2, y = 3 in (1) y3 = 3x2 + C1 33 = 3(βˆ’2)2 + C1 27 = 3 Γ— 4 + C1 27 βˆ’ 12 = C1 15 = C1 C1 = 15 Putting C1 in (1) y3 = 3x2 + 15 y = "(3x2 + " γ€–"15)" γ€—^(𝟏/πŸ‘) " "is the particular solution of the equation.

Davneet Singh's photo - Teacher, Engineer, Marketer

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.