# Example 18 - Chapter 9 Class 12 Differential Equations (Term 2)

Last updated at Aug. 20, 2021 by Teachoo

Examples

Example 1 (i)

Example 1 (ii) Important

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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

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Example 18 Important You are here

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Example 25 Deleted for CBSE Board 2023 Exams

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Example 28 Important

Chapter 9 Class 12 Differential Equations

Serial order wise

Last updated at Aug. 20, 2021 by Teachoo

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