AP EAMCET202422 May 2024Evening ShiftMathematicsDifferential EquationsActual
The differential equation of the family of hyperbola having their centres at origin and their axes along the coordinates axes is
Options
- Ax y y₂+x y₁^2-y y₁=0
- Bx y₂-x y y₁^2+y y₁=0
- Cx y y₂+x y₁^2+y y₁=0
- Dx y₂+x y₁^2-y y₁=0
Correct answer
A. x y y₂+x y₁^2-y y₁=0
Step-by-step solution
Let equation of hyperbola be x^2 a^2 + y^2 b^2 =1 2 x a^2 + 2 y b^2 d y d x =0 y x ( d y d x )= -b^2 a^2 Differentiate w.r.t. x, y x ( d^2 y d x^2 )+ x ( d y d x )^2-y d y d x x^2 =0 x y y₂+x (y₁ )^2-y y₁=0