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AP EAMCET2006MathematicsDifferential Equations

The solution of (1+x^2 ) d y d x +2 x y-4 x^2=0 is :

Options

  1. A3 x (1+y^2 )=4 y^3+c
  2. B3 y (1+x^2 )=4 x^3+c
  3. C3 x (1-y^2 )=4 y^3+c
  4. D3 y (1+y^2 )=4 x^3+c

Correct answer

B. 3 y (1+x^2 )=4 x^3+c

Step-by-step solution

(1+x^2 ) d y d x +2 x y-4 x^2=0 d y d x + ( 2 x 1+x^2 ) y= 4 x^2 1+x^2 On comparing with d y d x +P y=Q , we get P= 2 x 1+x^2 , Q= 4 x^2 1+x^2 I.F. =e^ P d x =e^ (1+x^2 ) =1+x^2 The solution is y (I.F.) = Q (I. F. ) d x+c₁ y (1+x^2 )= 4 x^2 (1+x^2 ) (1+x^2 ) d x+C₁ y (1+x^2 )= 4 x^3 3 +c₁ 3 y (1+x^2 )=4 x^3+c

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