Check sibling questions

Ex 9.5, 9 - Show homogeneous: y dx + x log (y/x) dy - 2x dy = 0 - Solving homogeneous differential equation

Ex 9.5, 9 - Chapter 9 Class 12 Differential Equations - Part 2
Ex 9.5, 9 - Chapter 9 Class 12 Differential Equations - Part 3
Ex 9.5, 9 - Chapter 9 Class 12 Differential Equations - Part 4
Ex 9.5, 9 - Chapter 9 Class 12 Differential Equations - Part 5
Ex 9.5, 9 - Chapter 9 Class 12 Differential Equations - Part 6

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Transcript

Ex 9.5, 9 In each of the Exercise 1 to 10 , show that the given differential equation is homogeneous and solve each of them. + 2 =0 Step 1 : Find + 2 =0 dy log 2 = y dx = log 2 = 2 log = 2 log Step 2. Putting F(x , y) = and finding F( x, y) F(x, y) = 2 log ( , ) = 2 log = 2 log = ( , ) Thus, F(x, y) is a homogenous equation function of order zero Therefore is a homogenous differential equation Step 3 : Solving by putting y = vx Putting y = vx Diff w.r.t.x = x + v = x + v Putting value of and y = vx in (1) = 2 log v + = 2 v + = 2 log = 2 log v = 2 + log 2 log = log 2 log 2 log log dv = Integrating both sides 2 log log dv = 2 log (1 log ) dv = log x + log c 1 + 1 log (1 log ) = log x + log c 1 ( )(1 log ) 1 = log x + log c 1 ( log 1) 1 = log x + log c ( log 1) log v = log x + log c Put t = log v 1 dt = 1 dv So, our equation becomes log v = log x + log c log t log v = log x + log c Putting value of t log (log v 1) log v + = log x + log c log (log v 1) = log x + log c + log v log (log v 1) = log C xv Putting value of v = log log 1 = log log log 1 = log log 1 = cy cy = log 1

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.