Ex 9.5, 10 - Chapter 9 Class 12 Differential Equations

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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