# Example 18

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 18 Show that the family of curves for which the slope of the tangent at any point , on its 2 + 2 2 , is given by 2 2 = We know that the slope of the tangent at , of a curve is Given slope of tangent at , is 2 + 2 2 Therefore = 2 + 2 2 Step 1: Find = 2 + 2 2 Step 2: Put = F So, F = 2 + 2 2 Finding F , F , = 2 + 2 2 = 2 2 + 2 2 2 2 = 2 2 + 2 2 2 = 2 + 2 2 = F , So , F , = F , = F , So , F , is homogeneous function of degree zero, Therefore given equation is a homogeneous differential equation Step 3: Solving by putting = = 2 + 2 2 Put = Diff. w.r.t. = = + = + Putting values and y in (i) v + = 2 + ( ) 2 2 ( ) v + = 2 + 2 2 2 2 v + = 2 + 2 2 2 2 . 2 2 v + = 2 + 2 2 2 2 2 2 2 v + = 2 + 2 2 2 2 2 2 2 = 2 + 2 2 2 2 2 2 2 = 2 2 2 2 2 = 2 1 2 2 . 2 = 1 2 2 = 1 2 2 . 1 2 1 2 = 2 2 1 = 2 2 1 = Integrating Both Sides 2 2 1 = 2 2 1 = 2 2 1 = + Solving Put 2 1= Diff. w.r.t. 2 1 = 2 = = 2 2 2 1 = 2 2 = = log Putting t = v2 1 = log 2 1 From (2) 2 2 1 = + log 2 1 = + 1 Putting = or = log 2 1 = + 1 log 2 1 = + 1 log 2 1 + =+ 1 2 1 = 1 2 2 1 = 1 Putting 1= log 2 2 1 = log 1 Removing log 2 2 1 = 1 2 2 = 1 2 = 1 2 2 = 1 2 2 = 1 2 2 = 1 Put = 1 = Hence Proved

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

Ex 9.4, 14 Important

Example 17 Important

Example 18 Important You are here

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.