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AP EAMCET20226 Jul 2022Evening ShiftMathematicsDifferential EquationsActual

Every curve represented by the general solution of d y d x = x x y^3 e^ y^2-5 =0 cuts every curve represented by the general solution of d y d x + y^3 e^ y^2-5 x x =0 at angle . Then, 4 - 2 =

Options

  1. A2
  2. B2
  3. C3 2

Correct answer

C. 3 2

Step-by-step solution

Given, d y d x = x x y^3 e^ y^2-5 Slope of this curve is m₁= x x y^3 e^ y^2-5 and d y d x + y^3 e^ y^2-5 x x =0 d y d x =- y^3 e^ y^2-5 x x Slope of this curve is m^2= -y^3 e^ y^2-5 x x Now, m₁ m₂= x x y^3 e^ y^2-5 ( -y^3 e^ y^2-5 x x )=-1 = 2 Now, 4 - 2 =(4) ( 2 )- 2 =2 - 2 = 3 2

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