







Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Examples
Example 1 (ii) Important
Example 1 (iii) Important
Example 2
Example 3 Important
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Example 5
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Example 7 Important
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Example 10 Important
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Example 13 Important You are here
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Example 15 Important
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Example 22 Important
Question 1 Deleted for CBSE Board 2024 Exams
Question 2 Deleted for CBSE Board 2024 Exams
Question 3 Important Deleted for CBSE Board 2024 Exams
Question 4 Deleted for CBSE Board 2024 Exams
Question 5 Deleted for CBSE Board 2024 Exams
Question 6 Deleted for CBSE Board 2024 Exams
Last updated at May 29, 2023 by Teachoo
Example 13 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