Example 17 - Show 2y e x/y dx + (y - 2x ex/y) dy = 0, particular - Examples

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Example 17 Show that the differential equation 2 + 2 =0 is homogeneous and find its particular solution , given that, =0 when =1 Step 1: Find 2 + 2 =0 2 = 2 2 = 2 = 2 2 Step 2: Put F , = and find F , F , = 2 2 Finding F , F , = 2 2 = 2 . 2 = 2 2 = F , So, F , = F , = F , Thus , F , is a homogeneous function of degree zero Therefore given differential equation is homogeneous differential equation Step 3: Solving by Putting = = 2 2 Put = Diff. w.r.t. = = . + = . + Putting values of and x in 1 = 2 2 + = 2 1 2 = 2 1 2 = 2 1 2 2 = 1 2 = 1 2 2 = Integrating Both Sides 2 = 2 = log + Putting = 2 = + 2 + = Given that at =0 , =1 Putting =0 and =1 in (2) 2 0 1 1 = 2 1+0= =2 Put Value of in (2) i.e., 2 + = 2 + log = c + log = 2 is the particular solution of given differential equation

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.