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AP EAMCET20228 Jul 2022Morning ShiftMathematicsDifferential EquationsActual

If the differential equation obtained by eliminating A,B from y= ( ⁻¹ x )^2+A ⁻¹ x+B is (a-x^2 ) y^ -x y^ =b , then b+a b-a =

Options

  1. A2
  2. B-2
  3. C3
  4. D-3

Correct answer

C. 3

Step-by-step solution

we are given that y= ( ⁻¹ x )^2+A ⁻¹ x+B ...(i) y ^1=2 ⁻¹( x ) 1 1- x ^2 - A 1- x ^2 ...(ii) = A =2 ⁻¹ z - 1- x ^2 , y ^1 Now y^1= 2 ⁻¹(x)-A 1-x^2 y ^4= 2 1- x ^2+2 x ⁻¹ x - Ax (1+ x ^2 )^ 3 / 2 =2 1- x ^2 +2 x ⁻¹ x -2 x ⁻¹ x+x y^1 1-x^2 (1-x^2 )^ 3 / 2 aligned & y^ = 2 1-x^2 +x y^ 1-x^2 (1-x^2 )^ 3 / 2 & y^ = 2+x y^ (1-x^2 ) & y^ = (1-x^2 ) y^ -x y^ =2 aligned Now, b + a b - a = 2+1 2-1 =3

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