Slide1.JPG

Slide2.JPG
Slide3.JPG Slide4.JPG Slide5.JPG

  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise

Transcript

Ex 9.5, 10 In each of the Exercise 1 to 10 , show that the given differential equation is homogeneous and solve each of them. 1+ + 1 =0 Step 1 : Find 1+ + 1 = 0 1+ dx = 1 = 1 1 + Step 2 : Put = F(x, y) and find F( x, y) F(x, y) = 1 1 + F( x, y) = 1 1 + = 1 1 + = ( , ) 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) = 1 1 + v + y = 1 1 + v + y = 1 1 + y = + 1 + v y = + 1 + y = + 1 + 1 + + dv = Integrating both sides 1+ + dv = 1 + + dv = log + log Put v + ev = t (1 + ev) dv = dt Thus, our equation becomes = log + log log = log + log Put value of t log (v + ev) = log y + log c log (v + ev) + log y = log c log y (v + ev) + log c Put value of v = log y e log y + e = log c y + e = c x + y = C

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
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.