# Example 13

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 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.

Chapter 9 Class 12 Differential Equations

Example 1
Important

Ex 9.1, 11 Important

Ex 9.1, 12 Important

Example 7 Important

Ex 9.3, 7 Important

Ex 9.3, 10 Important

Example 13 Important You are here

Ex 9.4, 14 Important

Example 17 Important

Example 18 Important

Ex 9.5, 8 Important

Ex 9.5, 15 Important

Example 22 Important

Ex 9.6, 7 Important

Ex 9.6, 13 Important

Ex 9.6, 14 Important

Example 25 Important

Example 27 Important

Example 28 Important

Misc 6 Important

Misc 11 Important

Misc 12 Important

Misc 13 Important

Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

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.